qudrature with tolerance in matlab

One way to perform numerical integration in Matlab is by using the functions quad or quadl. To compute the definite integral of a function f over an interval [a,b], you can use the following syntax:

main.m
quad(f,a,b)
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or

main.m
quadl(f,a,b)
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where f is a function handle or a function defined in a separate file, and a and b are the lower and upper limits of integration.

To control the accuracy of the integration, you can specify a tolerance with the optional parameter tol. The tolerance determines the maximum allowed absolute error in the approximation of the integral.

For example, to compute the integral of the function f(x) = exp(x) - 1 over the interval [0,1] with a tolerance of 1e-6, you can use the following code:

main.m
f = @(x) exp(x) - 1;
a = 0;
b = 1;
tol = 1e-6;

I = quad(f,a,b,tol)
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or

main.m
I = quadl(f,a,b,tol)
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The output I is the approximate value of the integral, computed with the specified tolerance.