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Question

If I=π/3π/6dx1+tanx then I equals

A
π12
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B
π6
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C
π4
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D
π3
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Solution

The correct option is B π12
We can write
I=π/3π/6cosxcosx+sinxdx(1)
Using baf(x)dx=baf(a+bx)dx,
We can write I=π/3π/6cos(π/2x)cos(π/2x)+sin(π/2x)dx
I=π/3π/6sinxsinx+cosxdx(2)
Adding (1) and (2), we get
2I=π/3π/6dx=x]π/3π/6=π6
I=π/12

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