TIFind the approximations or Map and So for Je$32$ sin$($x$)$ dx$.($Round your answers to six decimal places.$)$T$10=$M$10=510=63\mathrm{.}47275364\mathrm{.}26394964\mathrm{.}003505$Find the corresponding errors Ef$,$ Em$,$ and Eg$.($Round your answers to six decimal places.$)$ET $=$EM $=$Es $=0\mathrm{.}527247($b$)$ Compare the actual errors in part $($a$)$ with the error estimates found by using the smallest possible values for K in the theorem about error bounds for trapezoidal and midpoint rules and the theorem about error bound for Simpson's rule. Round your answers to six decimal places.$)$LET $0\mathrm{.}4134170\mathrm{.}005440$lEsl$($c$)$ Using the values of K from part $($b$),$ how large do we have to choose n so that the approximations T$,,$ M$,,$ and S$,$ to the integral in part $($a$)$ are accurate to within $0\mathrm{.}00001?$For Then $=$For M$,$ n $=$For Son $=$