Evaluate the integral.
-$$\int _ { 0 } ^ { 2 } \int _ { 0 } ^ { 8 } ( x + y ) d x d y$$
A) 5
B) 480
C) 80
D) 30

Question

Quizplus · Accepted Answer

We can evaluate the integral using the following steps:

\begin{align*}
\int_{0}^{2}\int_{0}^{8} (x+y) dxdy &= \int_{0}^{2} \left[\frac{1}{2}x^2+xyight]_{x=0}^{x=8} dy \
&= \int_{0}^{2} (32+8y) dy \
&= \left[32y+4y^2ight]_{y=0}^{y=2} \
&= 80
\end{align*}

Therefore, the best choice is $\boxed{	ext{(C) } 80}$.

Evaluate the Integral ∫02∫08(x+y)dxdy\int _ { 0 } ^ { 2 } \int _ { 0 } ^ { 8 } ( x + y ) d x d y∫02​∫08​(x+y)dxdy

Evaluate the Integral $\int _ { 0 } ^ { 2 } \int _ { 0 } ^ { 8 } ( x + y ) d x d y$