Use Monte$-$Carlo simulation to compute the integral:

$I={\displaystyle \underset{3}{\overset{8}{}}}(cos(x)+e^{2x}+2x)dx$

Test how many i$.$i$.$d$.$ r$.$v$.\text{'}$s are needed to achieve relative accuracy $0\mathrm{.}1,0\mathrm{.}01,$ and $0\mathrm{.}001.$

The relative accuracy is defined as $|hat(I)-I\frac{|}{\text{I}},$ where hat$(I)$ is the estimate you obtained. Note

that you may find a different answer whenever you have a different run of your code.

Please report the average number of i$.$i$.$d$.$ r$.$v$.\text{'}$s over at least $10$ runs needed to achieve the

prescribed relative accuracy. You can use whatever general programming language

$($Python$/$C$++/$VB$/$Matlab$/$Java$/$EXCEL$)$ that you are familiar with to write the code. The

code is required as part of the answers; in addition, you have to include the necessary

description of how the answers are obtained. $(6$ points$)$