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Question

The value of ππcos2x1+axdx, a>0, is

A
π2
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B
aπ
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C
2π
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D
πa
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Solution

The correct option is A π2
Let, f(x)=ππcos2x1+axdx(a>0) ..(1)

f(x)=ππcos2x1+axdx
baf(x)dx=baf(a+bx)

f(x)=ππaxcos2x1+axdx ...(2)
Adding (1) and (2), we get
2f(x)=ππcos2xdx=2π0cos2xdx
=2f(x)=4×12×π2
f(x)=π2
Ans: A

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