Evaluate $\int _ { - 1 } ^ { 1 } x ^ { 11 } d x$ .
A) 0
B) $\frac { 1 } { 11 }$
C) $\frac { 1 } { 22 }$
D) $- \frac { 1 } { 22 }$

Name: Evaluate $\int _ { - 1 } ^ { 1 } x ^ { 11 } d x$ . A) 0 B) $\frac { 1 } { 11 }$ C) $\frac { 1 } { 22 }$ D) $- \frac { 1 } { 22 }$
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Question

Quizplus · Accepted Answer

The integral of an odd function over a symmetric interval around zero is always zero. Since $x^{11}$ is an odd function (because 11 is odd), its integral from $-1$ to $1$ is $0$.

Evaluate ∫−11x11dx\int _ { - 1 } ^ { 1 } x ^ { 11 } d x∫−11​x11dx

Evaluate $\int _ { - 1 } ^ { 1 } x ^ { 11 } d x$