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Question

If  π0xf(sin x)dx=Aπ20f(sin x)dx, then A is equals to


Your Answer
A
0
Correct Answer
B
π
Your Answer
C
π4
Your Answer
D
2π

Solution

The correct option is C π
Let I=π0xf(sinx)dx     (1)
I=π0(πx)f[sin(πx)]dx
I=π0(πx)f[sin(x)]dx    (2)
Adding    (1) and (2)
2I=ππ0f(sinx)dx
2I=2ππ20f(sinx)dx
I=ππ20f(sin x)dx
Aπ20f(sin x)dx=ππ20 f(sin x)dx
A=π

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