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Question

The value of integral 10sin1xsin1x+cos12xx2dx is

A
1
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B
12
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C
2
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D
0
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Solution

The correct option is B 12
Let I=10sin1xsin1x+cos12xx2dx

I=10sin1xsin1x+sin1(1x)dx ------(1)

(since, cos12xx2=cos12(1x)(1x)2=cos11x2=sin1(1x)

I=10sin1(1x)sin1(1x)+sin1xdx ------(2)

(1)+(2)2I=101dx=(10)=1

I=12

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