Description
Implement the following numerical methods for approximating integrals: (i)
trapezoidal rule, (ii) Simpson’s rule, and (iii) Clenshaw-Curtis rule. (Code
for generating the points and weights of the Clenshaw-Curtis rule is available
on Canvas.)
Using calculus, compute the definite integral of f(x) = cos(3πx) on the
interval [−1, 1]. Run a convergence study on the three numerical methods
and identify the asymptotic regime and the rate of convergence for each
method. FOR FUN: Change the integration interval to [−π, π] and repeat
the study. What changes?
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