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Question

ππ2x(1+sinx)1+cos2xdx is


Your Answer
A
π24
Correct Answer
B
π2
Your Answer
C
zero
Your Answer
D
π2

Solution

The correct option is B π2
Let I=ππ2x(1+sin x)1+cos2xdx
=ππ2x1+cos2xdx+ππ2xsinx1+cos2xdx
I=4π0x sin x1+cos2xdx(1)
I=4π0(πx)sin(πx)1+cos2(πx)dx(2)
From (1) and (2)
I=4ππ0sinx1+cos2xdxI
I=2ππ0sinx1+cos2xdx
Put cos x=tsin x dx =dt
I=2π1111+t2dt=π2

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