{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-09-03T01:10:40.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-09-03T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":61461,"title":"Calculate integrals using numerical methods 3.","description":"Now let's compare the 2 previous rules. Using the \"Simpson 1/3\" rule and the trapezoidal rule, NOT THE SIMPLE ONES, calculate the following integral:\r\n\r\nFurther explanations:\r\n1)the limits(a,b) will be given.\r\n2)The number of subspaces(n) of [a,b] will also be given.\r\n3)I1 is the integral of the Simpson rule. I2 the integral of the trapezoidal rule.\r\n4)ROUND THE RESULTS TO 4 DECIMAL PLACES!!!!!!!!!!!!\r\nGOOD LUCK!!!!!!!!!!!!!!!!!!!!!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 277px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 138.5px; transform-origin: 469px 138.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 21px; text-align: left; transform-origin: 445px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNow let's compare the 2 previous rules. Using the \"Simpson 1/3\" rule and the trapezoidal rule, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eNOT THE SIMPLE ONES\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, calculate the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv 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\" width=\"69\" height=\"46\" style=\"width: 69px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFurther explanations:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1)the limits(a,b) will be given.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2)The number of subspaces(n) of [a,b] will also be given.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3)I1 is the integral of the Simpson rule. I2 the integral of the trapezoidal rule.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4)ROUND THE RESULTS TO 4 DECIMAL PLACES!!!!!!!!!!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!!!!!!!!!!!!!!!!!!!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [I1 I2] = CompareS_T(a,b,n)\r\n    \r\nend ","test_suite":"%%\r\na = 1; \r\nb = 5; \r\nn = 2;\r\nI1_correct = round(2/3*log(405),4);\r\nI2_correct = round(log(45),4);\r\n[I1, I2] = CompareS_T(a,b,n);\r\nassert(abs(I1 - I1_correct) \u003c 1e-4 \u0026\u0026 abs(I2 - I2_correct) \u003c 1e-4)\r\n%%\r\na = 2; \r\nb = 8; \r\nn = 4;\r\nI1_correct = 9.2449;\r\nI2_correct = 9.1804;\r\n[I1, I2] = CompareS_T(a,b,n);\r\nassert(abs(I1 - I1_correct) \u003c 1e-4 \u0026\u0026 abs(I2 - I2_correct) \u003c 1e-6)\r\n%%\r\na = 5;\r\nb = 15;\r\nn = 8;\r\nI1_correct = 22.5734;\r\nI2_correct = 22.5563;\r\n[I1, I2] = CompareS_T(a,b,n);\r\nassert(abs(I1 - I1_correct) \u003c 1e-4 \u0026\u0026 abs(I2 - I2_correct) \u003c 1e-6)\r\n%%\r\ncode = fileread(which('CompareS_T'));\r\nhas_if = ~isempty(regexp(code, '\\bif\\b', 'once'));\r\nassert(~has_if, 'Using \"if\" is not allowed!')","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5158730,"edited_by":5158730,"edited_at":"2026-08-30T13:00:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2026-08-30T13:00:07.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-08-30T12:55:50.000Z","updated_at":"2026-08-31T15:31:58.000Z","published_at":"2026-08-30T13:00:07.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNow let's compare the 2 previous rules. Using the \\\"Simpson 1/3\\\" rule and the trapezoidal rule, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOT THE SIMPLE ONES\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, calculate the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$$ \\\\int_{a}^{b} lnx \\\\ dx $$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFurther explanations:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1)the limits(a,b) will be given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2)The number of subspaces(n) of [a,b] will also be given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3)I1 is the integral of the Simpson rule. I2 the integral of the trapezoidal rule.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4)ROUND THE RESULTS TO 4 DECIMAL PLACES!!!!!!!!!!!!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGOOD LUCK!!!!!!!!!!!!!!!!!!!!!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"problems":[{"id":61461,"title":"Calculate integrals using numerical methods 3.","description":"Now let's compare the 2 previous rules. Using the \"Simpson 1/3\" rule and the trapezoidal rule, NOT THE SIMPLE ONES, calculate the following integral:\r\n\r\nFurther explanations:\r\n1)the limits(a,b) will be given.\r\n2)The number of subspaces(n) of [a,b] will also be given.\r\n3)I1 is the integral of the Simpson rule. I2 the integral of the trapezoidal rule.\r\n4)ROUND THE RESULTS TO 4 DECIMAL PLACES!!!!!!!!!!!!\r\nGOOD LUCK!!!!!!!!!!!!!!!!!!!!!","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(33, 33, 33); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 277px; display: block; min-width: 0px; padding-block-start: 0px; padding-inline-start: 2px; padding-left: 2px; padding-top: 0px; perspective-origin: 469px 138.5px; transform-origin: 469px 138.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 21px; text-align: left; transform-origin: 445px 21px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eNow let's compare the 2 previous rules. Using the \"Simpson 1/3\" rule and the trapezoidal rule, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003eNOT THE SIMPLE ONES\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, calculate the following integral:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 23px; text-align: left; transform-origin: 445px 23px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"vertical-align:-19px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"69\" height=\"46\" style=\"width: 69px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFurther explanations:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e1)the limits(a,b) will be given.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e2)The number of subspaces(n) of [a,b] will also be given.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e3)I1 is the integral of the Simpson rule. I2 the integral of the trapezoidal rule.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e4)ROUND THE RESULTS TO 4 DECIMAL PLACES!!!!!!!!!!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 445px 10.5px; text-align: left; transform-origin: 445px 10.5px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eGOOD LUCK!!!!!!!!!!!!!!!!!!!!!\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [I1 I2] = CompareS_T(a,b,n)\r\n    \r\nend ","test_suite":"%%\r\na = 1; \r\nb = 5; \r\nn = 2;\r\nI1_correct = round(2/3*log(405),4);\r\nI2_correct = round(log(45),4);\r\n[I1, I2] = CompareS_T(a,b,n);\r\nassert(abs(I1 - I1_correct) \u003c 1e-4 \u0026\u0026 abs(I2 - I2_correct) \u003c 1e-4)\r\n%%\r\na = 2; \r\nb = 8; \r\nn = 4;\r\nI1_correct = 9.2449;\r\nI2_correct = 9.1804;\r\n[I1, I2] = CompareS_T(a,b,n);\r\nassert(abs(I1 - I1_correct) \u003c 1e-4 \u0026\u0026 abs(I2 - I2_correct) \u003c 1e-6)\r\n%%\r\na = 5;\r\nb = 15;\r\nn = 8;\r\nI1_correct = 22.5734;\r\nI2_correct = 22.5563;\r\n[I1, I2] = CompareS_T(a,b,n);\r\nassert(abs(I1 - I1_correct) \u003c 1e-4 \u0026\u0026 abs(I2 - I2_correct) \u003c 1e-6)\r\n%%\r\ncode = fileread(which('CompareS_T'));\r\nhas_if = ~isempty(regexp(code, '\\bif\\b', 'once'));\r\nassert(~has_if, 'Using \"if\" is not allowed!')","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":5158730,"edited_by":5158730,"edited_at":"2026-08-30T13:00:36.000Z","deleted_by":null,"deleted_at":null,"solvers_count":4,"test_suite_updated_at":"2026-08-30T13:00:07.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2026-08-30T12:55:50.000Z","updated_at":"2026-08-31T15:31:58.000Z","published_at":"2026-08-30T13:00:07.000Z","restored_at":null,"restored_by":null,"spam":null,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNow let's compare the 2 previous rules. Using the \\\"Simpson 1/3\\\" rule and the trapezoidal rule, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eNOT THE SIMPLE ONES\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e, calculate the following integral:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e$$ \\\\int_{a}^{b} lnx \\\\ dx $$\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFurther explanations:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e1)the limits(a,b) will be given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e2)The number of subspaces(n) of [a,b] will also be given.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e3)I1 is the integral of the Simpson rule. I2 the integral of the trapezoidal rule.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e4)ROUND THE RESULTS TO 4 DECIMAL PLACES!!!!!!!!!!!!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eGOOD LUCK!!!!!!!!!!!!!!!!!!!!!\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"errors":[],"facets":[[],[{"value":"medium","count":1,"selected":false}]],"term":"tag:\"numeric analysis\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}