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Question

lf 10tan1xxdx=kπ/20xsinxdx, then the value of k is

A
1
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B
14
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C
4
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D
2
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Solution

The correct option is A 2
Let I=π20xsinxdx
Substitute tan(x2)=t12sec2(x2)dx=dt
gives sinx=2t1+t2,dx=2dt1+t2
I=102tan1t2t1+t22dt1+t2=210tan1ttdt=210tan1xxdxk=2

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