Use the Trapezoidal Rule with n = 4 steps to estimate the integral.
-$$\int _ { 0 } ^ { 2 } \left( x ^ { 4 } + 8 \right) d x$$
A) $\frac { 497 } { 16 }$
B) $\frac { 269 } { 12 }$
C) $\frac { 369 } { 16 }$
D) $\frac { 369 } { 8 }$

Question

Quizplus · Accepted Answer

Using the Trapezoidal Rule with n = 4, we have:
\begin{align*}
\int _ { 0 } ^ { 2 } \left( x ^ { 4 } + 8 ight) d x &\approx \frac{2-0}{2n}\left[\left(0^4+8ight)+2\left(1^4+8ight)+2\left(2^4+8ight)+\left(2^4+8ight)ight]\
&= \frac{1}{4}\left[ 8 + 2\cdot9 + 2\cdot24 + 24 ight]\
&= \frac{369}{16}
\end{align*}
Therefore, the best choice is C.

Use the Trapezoidal Rule with N = 4 Steps to Estimate