Evaluate the following iterated integral. $$\int _ { 2 } ^ { 3 } \int _ { y } ^ { 7 y } \left( 7 + 3 x ^ { 2 } + 3 y ^ { 2 } \right) d x d y$$
A) 5,901
B) 5,931
C) 5,955
D) 5,970
E) 6,017

Question

Quizplus · Accepted Answer

First, integrate with respect to $x$ from $y$ to $7y$, then integrate the resulting expression with respect to $y$ from 2 to 3. The final result is 5,955.

Evaluate the Following Iterated Integral ∫23∫y7y(7+3x2+3y2)dxdy\int _ { 2 } ^ { 3 } \int _ { y } ^ { 7 y } \left( 7 + 3 x ^ { 2 } + 3 y ^ { 2 } \right) d x d y∫23​∫y7y​(7+3x2+3y2)dxdy

Evaluate the Following Iterated Integral $\int _ { 2 } ^ { 3 } \int _ { y } ^ { 7 y } \left( 7 + 3 x ^ { 2 } + 3 y ^ { 2 } \right) d x d y$