Decide whether the integral converges. If the integral converges, compute its value. $\int _ { - \infty } ^ { \infty } 9 x e ^ { - 6 x ^ { 2 } } \mathrm {~d} x$
A)6
B) 9
C) 0
D) 18
E) diverges

Question

Decide whether the integral converges. If the integral converges, compute its value.   $\int _ { - \infty } ^ { \infty } 9 x e ^ { - 6 x ^ { 2 } } \mathrm {~d} x$  
A)6
B) 9
C) 0
D) 18
E) diverges

Quizplus · Accepted Answer

The integral of an odd function over a symmetric interval around zero is zero. Since $9xe^{-6x^2}$ is an odd function (i.e., $f(-x) = -f(x)$), its integral from $-\infty$ to $\infty$ is 0.

Decide Whether the Integral Converges ∫−∞∞9xe−6x2 dx\int _ { - \infty } ^ { \infty } 9 x e ^ { - 6 x ^ { 2 } } \mathrm {~d} x∫−∞∞​9xe−6x2 dx

Decide Whether the Integral Converges $\int _ { - \infty } ^ { \infty } 9 x e ^ { - 6 x ^ { 2 } } \mathrm {~d} x$