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Question

If I=10cot1 (1x+x2) dx=k10tan1 x dx, then the value of k equals

A
1
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B
2
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C
π
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D
2π
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Solution

The correct option is B 2
We have,
I=10cot1 (1x+x2) dx=k10tan1 x dx10tan1 (1(1x+x2)} dx=k10tan1 x dx10tan1 (11x(1x)} dx=k10tan1 x dx10tan1 ((1x)+x1x(1x)} dx=k10tan1 x dx10(tan1 (1x)+tan1 x}dx=k10tan1 x dx10tan1 (1x) dx+10tan1 x dx=k10tan1 x dx10tan1 (1(1x)] dx+10tan1 x dx=k10tan1 x dx10tan1 x dx+10tan1 x dx=k10tan1 x dx210tan1 x dx=k10tan1 x dxk=2

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