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Question

The value of ππcos2x1+axdx for a>0 is?

A
π
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B
aπ
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C
π2
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D
2π
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Solution

The correct option is C π2
Let I=ππcos2x1+axdx ...(1)
Using property baf(x)dx=baf(a+bx)dx
I=ππcos2(π+πx)1+a(π+πx)dx=ππaxcos2x1+axdx ...(2)
Adding (1) and (2), we get
2I=ππcos2xdx=[12(x+sinxcosx)]ππ=12(π+0+π0)=πI=π2

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