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Question

a0dxa+a2x2 is equal to

A
π2+1
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B
π21
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C
1π2
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D
none of these
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Solution

The correct option is C π21
Let I=a0dxa+a2x2=π/20acosθdθa+acosθ
By putting x=asinθdx=acosθdθ
I=π/20cosθ1+cosθdθ=π/20(111+cosθ)dθ
=π/20dθ12π/20sec2θ2dθ
=[θtanθ2]π/20=π2tanπ4=(π21)

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