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Question

Evaluate the integral
π/2011+4tanxdx

A
π/4
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B
π/2
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C
0
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D
π/3
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Solution

The correct option is A π/4

I=π2011+4tanxdx

a0f(x)dx=a0f(ax)dx

I=π2011+4tanxdx=π2011+4cotxdx=π204tanx4tanx+1dx=I

2I=π201dx

2I=π2

I=π4

π2011+4tanxdx=π4


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