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Question

2x-144. Thevalue of:tan-xī)-isdx is(A) 1(B) 0(C)-14

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Solution

The given integral is, I= 0 1 tan 1 ( 2x1 1+x x 2 )dx .

Solve the integral.

I= 0 1 tan 1 ( x( 1x ) 1+x( 1x ) )dx = 0 1 tan 1 xdx 0 1 tan 1 ( 1x )dx = 0 1 tan 1 xdx 0 1 tan 1 ( 1x1 )dx = 0 1 tan 1 xdx 0 1 tan 1 ( x )dx

Simplify further,

I= 0 1 tan 1 xdx 0 1 tan 1 xdx =0

Thus, option (B) is correct.


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