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Question: \(\int _ { - 3 } ^ { 3 } \frac { x ^ { 2 } \sin x } { 1 + x ^ { 6 } } d x =\)...

∫−33x2sin⁡x1+x6dx=\int _ { - 3 } ^ { 3 } \frac { x ^ { 2 } \sin x } { 1 + x ^ { 6 } } d x =

A

4

B

2

C

0

D

None of these

Answer

0

Explanation

Solution

∫−33x2sin⁡x1+x6dx=0\int _ { - 3 } ^ { 3 } \frac { x ^ { 2 } \sin x } { 1 + x ^ { 6 } } d x = 0. By the property of definite integral,

∫−aaf(x)dx=0\int _ { - a } ^ { a } f ( x ) d x = 0, whenf(x)=−f(−x)f ( x ) = - f ( - x ).