Evaluate $\int _ { - \pi } ^ { \pi } \sin ^ { 3 } ( x ) d x$
A) 1
B) 0
C) $1 / 2$
D) -1

Name: Evaluate $\int _ { - \pi } ^ { \pi } \sin ^ { 3 } ( x ) d x$ A) 1 B) 0 C) $1 / 2$ D) -1
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Question

Quizplus · Accepted Answer

The integral of an odd function over a symmetric interval around zero is zero. Since $\sin^3(x)$ is an odd function and the interval is symmetric around zero, the integral evaluates to 0.

Evaluate ∫−ππsin⁡3(x)dx\int _ { - \pi } ^ { \pi } \sin ^ { 3 } ( x ) d x∫−ππ​sin3(x)dx

Evaluate $\int _ { - \pi } ^ { \pi } \sin ^ { 3 } ( x ) d x$