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Question

Evaluate:ππ(1x2)sin xcos2x dx

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Solution

We know that
aaf(x) dx=2a0f(x) dx,if f(x) is even0,if f(x) is odd

Here, f(x)=(1x2)sin xcos2x
f(x)=(1(x)2)sin (x)cos2(x)
=(1x2)sin xcos2x=f(x)
f(x) is an odd function.
ππ(1x2)sin xcos2x dx=0

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