What is the difference between int and integral.

Hello everyone

I want to get explained how to decide wheather use function "int" or "integral".

What is the basic difference between them? will they give same answer for a given function?

Thank you very much in advance.

[Ashwani Kumar MAlviya]

n = length(FC); % Calculates the Number of consistant respondents(Nt)
x = sum(FC == mode(FC)); % Calculates the Number of respondents answered mode
p = 1/17; % Probability of selecting mode(Pi)
mu = n*p; 
sigma = sqrt(n.*p.*(1 - p)); % Standerd deviation

if n<= 20
    i = 0;
    syms i
    alfa = double(symsum((factorial(n)/(factorial(i)*factorial(n-i))*(p).^(i)*(1-p).^(n-i)), i, 0, x)); % 0 = constant, 2 = x
%     beta1 = symsum((factorial(n)/(factorial(i)*factorial(n-i))*(1-1/17).^(i)*(1/17).^(n-i)), i, 0, n-x);
%     power = 1-beta1;

elseif n>20
    syms y
    f = (-(y-mu)^2)/(2*sigma^2); % 5.05 is 2*sigma^2, & 2.7 = mu
    fun = (1/(sigma*2.5))*(exp(f)); % 0.2516 = 1/(sigma*2.5), e = 2.71
    a = -inf;
    b = x; %x; % number of respondent selected mode
    alfa = double(int(fun, a, b));
                %%% ^ if I am using integral here, I am getting different answer. what mistake am I making conceptually.

Answer 1

[Star Strider]

The int function integrates symbolic expressions (or does its best, consdidering that not all expressions have analytic integrals).

The integral function is for numeric functions, usually anonymous functions.

The documentation pages for those functions explain them better than I can, so I provided links to them.

[A. Wunsch]

good thanks

[Star Strider]

A. Wunsch —

My pleasure!

(A vote is always appreciated!)

[Temi]

Hello @Star Strider!!! when evaluating definite integrals using int, what integration scheme does the function use? trapezoid, rungekutta, quadrature, simpsons?

which is better to evaluate integrals numerically?; int or integral

[Torsten]

"int" tries to find an analytical antiderivative of your function. So it does not use any numerical integration scheme.

For the integration method of "integral", see

[1] L.F. Shampine “Vectorized Adaptive Quadrature in MATLAB®,” Journal of Computational and Applied Mathematics, 211, 2008, pp.131–140.

If the function does not look too complicated, try "int" first.

If no analytical antiderivative can be found using "int", use "integral".