Find the area under the curve given by $y=cos(x)+1($i$.$e$.$ above the $x$ axis$)$ for $|x|1.$

Use $1000$ random samplings of the rectangular area set by $|x|1$ and $0y2.$

Name your vectors $x$ and $y$ to make it possible for the MATLAB Grader to check your solution.

Your script must be vectorized. Do not use for$-$loops.

Provide the following two quantities:

$Na=$ the number of points that have landed under the curve $($do not count the points that land directly onto the curve$)$;

$Sa=$ the area under the curve.

Script $o.$

$N=1000$;

$x=2**rand(1,N)-1$;

$y=(rand(1,N))**2$;

$f=cos(**x)+1$;

under$\_$curve $Na=Sa=4**N\frac{a}{N}=y$;

$Na=$ sum$(unde{r}_c$urve$)$;

$Sa=4**N\frac{a}{N}$;

disp$([\text{'}Numberof$ points under the curve: $\text{'}$ num$2str(Na)])$;

disp$([\text{'}Estimated$ area under the curve: $\text{'}$ num$2str(Sa)])$;

disp$({[}^{\text{'}}x={[}^{\text{'}}$ num$2str(x\text{'})\text{'}]\text{'}\text{'}$;$\text{'}])$;

disp$({[}^{\text{'}}y={[}^{\text{'}}$ num$2str(y\text{'})\text{'}]\text{'}\text{'}$;$\text{'}])$;