Evaluate the following double integral: $\int _ { - 2 } ^ { 3 } \int _ { - 2 } ^ { 2 } x ^ { 2 } y ^ { 3 } d y d x$
A) $\frac { 1 } { 2 }$
B) 3
C) 0
D) The integral can't be evaluated.

Question

Quizplus · Accepted Answer

The integral of an odd function over a symmetric interval is zero. Since $y^3$ is an odd function and the interval for $y$ is symmetric about 0 (from -2 to 2), the integral evaluates to 0 regardless of the $x^2$ term.

Evaluate the Following Double Integral ∫−23∫−22x2y3dydx\int _ { - 2 } ^ { 3 } \int _ { - 2 } ^ { 2 } x ^ { 2 } y ^ { 3 } d y d x∫−23​∫−22​x2y3dydx

Evaluate the Following Double Integral $\int _ { - 2 } ^ { 3 } \int _ { - 2 } ^ { 2 } x ^ { 2 } y ^ { 3 } d y d x$