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Question

Question: \(\int _ { - a } ^ { a } \sin x f ( \cos x ) d x =\)...

∫−aasin⁡xf(cos⁡x)dx=\int _ { - a } ^ { a } \sin x f ( \cos x ) d x =

A

2∫0asin⁡xf(cos⁡x)dx2 \int _ { 0 } ^ { a } \sin x f ( \cos x ) d x

B

0

C

1

D

None of these

Answer

0

Explanation

Solution

I=∫−aasin⁡xf(cos⁡x)dxI = \int _ { - a } ^ { a } \sin x f ( \cos x ) d x

f(x)=sin⁡xf(cos⁡x)⇒f(−x)=−sin⁡xf(cos⁡x)f ( x ) = \sin x f ( \cos x ) \Rightarrow f ( - x ) = - \sin x f ( \cos x )

is an odd function

∴I=∫f(x)dx=0\therefore I = \int f ( x ) d x = 0.