calculate an integral using chebyshev polynomials in matlab

To calculate an integral using Chebyshev polynomials in MATLAB, you can use the chebfun package, which provides an easy and efficient way to work with functions represented as chebyshev polynomials.

First, you will need to define the function you want to integrate as a chebfun object, using the chebfun function:

main.m
f = chebfun(@(x) sin(x),[-1,1]);
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This creates a chebfun object that represents the function sin(x) over the interval [-1,1].

Next, you can use the chebint function to compute the integral of the chebfun object:

main.m
I = chebint(f);
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This returns another chebfun object representing the indefinite integral of f.

Finally, you can evaluate the definite integral over a given interval using the sum function applied to the chebfun object:

main.m
a = -1;
b = 1;
result = sum(I([a,b]));
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This computes the definite integral of sin(x) over [-1,1], and stores the result in the result variable.

Here's the full code:

main.m
f = chebfun(@(x) sin(x),[-1,1]);
I = chebint(f);
a = -1;
b = 1;
result = sum(I([a,b]));
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Note that this method can be used to compute the integral of any function represented as a chebfun object.