Evaluate the integral.
-$$\int _ { - \pi / 2 } ^ { \pi / 2 } \cos ^ { 5 } 8 x d x$$
A) 0
B) $- \frac { 2 } { 15 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 15 }$

Question

Quizplus · Accepted Answer

The integral of an odd function over a symmetric interval around zero is zero. Since $\cos^5(8x)$ is an even function, but the integral's bounds are symmetric around zero, the odd powers of sine that arise from integrating $\cos^5(8x)$ result in an overall integral of zero.

Evaluate the Integral ∫−π/2π/2cos⁡58xdx\int _ { - \pi / 2 } ^ { \pi / 2 } \cos ^ { 5 } 8 x d x∫−π/2π/2​cos58xdx

Evaluate the Integral $\int _ { - \pi / 2 } ^ { \pi / 2 } \cos ^ { 5 } 8 x d x$