Evaluate the iterated integral. $\int _ { 1 } ^ { 3 } \int _ { y } ^ { 3 } 8 x y d x d y$
A) $64$
B) $6$
C) $74$
D) $84$
E) $94$

Name: Evaluate the iterated integral. $\int _ { 1 } ^ { 3 } \int _ { y } ^ { 3 } 8 x y d x d y$ A) $64$ B) $6$ C) $74$ D) $84$ E) $94$
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Question

Quizplus · Accepted Answer

First, integrate with respect to $x$: $\int_{y}^{3} 8xy \, dx = 4y(3^2 - y^2)$. Then, integrate with respect to $y$ from 1 to 3: $\int_{1}^{3} 4y(9 - y^2) \, dy = 64$.

Evaluate the Iterated Integral ∫13∫y38xydxdy\int _ { 1 } ^ { 3 } \int _ { y } ^ { 3 } 8 x y d x d y∫13​∫y3​8xydxdy

Evaluate the Iterated Integral $\int _ { 1 } ^ { 3 } \int _ { y } ^ { 3 } 8 x y d x d y$