Cody

Problem 47043. Find the Arc Length of the Curve Defined by the Parametric Functions

Solution 3348168

Submitted on 23 Oct 2020 by Rafael S.T. Vieira
  • Size: 12
  • This is the leading solution.
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.

This solution is outdated. To rescore this solution, sign in.

Solve This Problem View on Solution Map

Test Suite

Test Status Code Input and Output
1   Pass
interval=[0,2*pi]; a=3; b=1; x = @(t)(a-b)*cos(t)+b*cos((a-b)/b*t); y = @(t)(a-b)*sin(t)-b*sin((a-b)/b*t); S = 16; assert(abs(arcLength(x,y,interval)-S)<1e-3)
2   Pass
interval=[0,2*pi]; a=5; b=1; x = @(t)(a-b)*cos(t)+b*cos((a-b)/b*t); y = @(t)(a-b)*sin(t)-b*sin((a-b)/b*t); S = 32; assert(abs(arcLength(x,y,interval)-S)<1e-3)
3   Pass
interval=[0,2*pi]; a=7; b=1; x = @(t)(a-b)*cos(t)+b*cos((a-b)/b*t); y = @(t)(a-b)*sin(t)-b*sin((a-b)/b*t); S = 48; assert(abs(arcLength(x,y,interval)-S)<1e-3)
4   Pass
interval=[0,6*pi]; a=7; b=3; x = @(t)(a-b)*cos(t)+b*cos((a-b)/b*t); y = @(t)(a-b)*sin(t)-b*sin((a-b)/b*t); S = 96; assert(abs(arcLength(x,y,interval)-S)<1e-3)
5   Pass
interval=[0,10*pi]; a=11; b=5; x = @(t)(a-b)*cos(t)+b*cos((a-b)/b*t); y = @(t)(a-b)*sin(t)-b*sin((a-b)/b*t); S = 240; assert(abs(arcLength(x,y,interval)-S)<1e-3)
6   Pass
interval=[0,2*pi]; x=@(t)5*(t-sin(t)); y=@(t)5*(1-cos(t)); S=40; assert(abs(arcLength(x,y,interval)-S)<1e-3)
7   Pass
interval=[0,100*pi]; a=pi; b=1; x = @(t)(a-b)*cos(t)+b*cos((a-b)/b*t); y = @(t)(a-b)*sin(t)-b*sin((a-b)/b*t); S = 856.288; assert(abs(arcLength(x,y,interval)-S)<1e-3)

Suggested Problems

More from this Author30

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!