Problem $1.-$ Given the integral below

$($Group $1$: Ramisa and Regine$){\displaystyle \underset{0}{\overset{\frac{}{4}}{}}}4si{n}^2(x)dx$

$($Group $2$: Lauren and Paula$){\displaystyle \underset{\frac{}{4}}{\overset{\frac{}{2}}{}}}4co{s}^2(x)dx$

$($Group $3$: Chelsea, Angeli and Bencheta$)$

${\displaystyle \underset{0}{\overset{\frac{}{4}}{}}}ta{n}^2(x)dx$

A$.$ Use the Simpson's method to estimate the integral above by dividing the interval into $50$ equals subintervals.

B$.$ Evaluate the integral using direct integration. Show your work.

C$.$ Calculate the absolute and relative errors of your estimation in part A

Please answer for Group $2$ ONLY