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Question

If Φ(x)=log(sin x)x,xn π, nϵ I and 313log(sin x)xdx=Φ(k)Φ(1) then the value of k is

A
27
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B
18
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C
9
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D
None of these
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Solution

The correct option is A 27
313 log(sin x3)xdx=271log(sinz)zdz
[putting x3=z3dx=dzx2]
=271Φ(z)dz=[Φ(z)]271=Φ(27)Φ(1)
k=27

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