Homework:

HW $8\mathrm{.}8-$

Question

Completed: $26$ of $31$

Numerical

Part $1$ of $4$

My score: $\frac{25\mathrm{.}57}{31}pts(22\mathrm{.}49\%)$

Integration

Apply Simpson's Rule to the following infegral. It is easiest to obtain the Simpson's Rule approximations from the Trapezold Rule approximations. Make a table showing the approximations and errors for $n=4,8,16,$ and $32.$ The exact value of the integral is given for computing the error.

${\displaystyle \underset{0}{\overset{}{}}}{e}^{-5t}sin6tdt=\frac{6}{61}(1-e^{-5})$

Complete the table below.

$($Type integers or decimals. Round to six decimal places as needed.$)$

$\backslash$table$[[n,T(n),S(n),\backslash$table$[[$Absolute Error$],[$in $T(n)$