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Question

a0dxx+a2x2 is

A
a24
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B
π2
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C
π4
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D
π
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Solution

The correct option is C π4
I=a0dxx+a2x2

Putting
x=asinθdx=acosθ dθ
When
x=0=asinθθ=0x=a=asinθθ=π2

So, the integral become,
I=π/20cosθdθsinθ+cosθ (1)
Using property,
I=π/20cos(π2θ)dθsin(π2θ)+cos(π2θ)I=π/20sinθdθcosθ+sinθ (2)

Adding (1) and (2),
2I=π/20sinθ+cosθsinθ+cosθdθI=12π/201 dθI=π4

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