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Question: \(\int _ { - 1 } ^ { 1 } \sin ^ { 11 } x d x\) is equal to...

∫−11sin⁡11xdx\int _ { - 1 } ^ { 1 } \sin ^ { 11 } x d x is equal to

A

1011⋅89⋅67⋅45⋅23\frac { 10 } { 11 } \cdot \frac { 8 } { 9 } \cdot \frac { 6 } { 7 } \cdot \frac { 4 } { 5 } \cdot \frac { 2 } { 3 }

B

1011⋅89⋅67⋅45⋅23⋅π2\frac { 10 } { 11 } \cdot \frac { 8 } { 9 } \cdot \frac { 6 } { 7 } \cdot \frac { 4 } { 5 } \cdot \frac { 2 } { 3 } \cdot \frac { \pi } { 2 }

C

1

D

0

Answer

0

Explanation

Solution

Since f(x)=sin⁡11xf ( x ) = \sin ^ { 11 } x is an odd function, therefore

∫−11sin⁡11xdx=0\int _ { - 1 } ^ { 1 } \sin ^ { 11 } x d x = 0.