Given the integral below:

$2$

$=(325)$

$0$

$[15$ marks$]$

Calculate $$ and compute the error and using the built in functions for the following:

$4\mathrm{.}1.$ Numerical integration using adaptive Clenshaw$$Curtis rule.

$(8)$

$4\mathrm{.}2.$ Numerical integration based on adaptive Gaussian quadrature.

$(6)$

$4\mathrm{.}3.$ Discuss your observation.

$(3)$

$[20$ marks$]$

Total $=[63$ Marks$]$