Evaluate the following double integral: $$\int _ { - 4 } ^ { 7 } \int _ { - 4 } ^ { 4 } x ^ { 4 } y ^ { 7 } d y d x$$
A) 4
B) The integral can't be evaluated.
C) $\frac { 1 } { 4 }$
D) 0

Question

Quizplus · Accepted Answer

The integral of an odd function over a symmetric interval is zero. Since $y^7$ is an odd function and the interval for $y$ is symmetric about 0 (from -4 to 4), the integral of $x^4y^7$ over this interval will be 0, regardless of the $x^4$ term.

Evaluate the Following Double Integral ∫−47∫−44x4y7dydx\int _ { - 4 } ^ { 7 } \int _ { - 4 } ^ { 4 } x ^ { 4 } y ^ { 7 } d y d x∫−47​∫−44​x4y7dydx

Evaluate the Following Double Integral $\int _ { - 4 } ^ { 7 } \int _ { - 4 } ^ { 4 } x ^ { 4 } y ^ { 7 } d y d x$