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Find the area bounded by y=tan^(-1)x , y...

Find the area bounded by `y=tan^(-1)x , y=cot^(-1)x ,a n dy-axis in the first quadrant.

Text Solution

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The correct Answer is:
`log sqrt(2)` sq. units

Intergrating along x-axis, we get
`A=overset(1)underset(0)int(cot^(-1)x-tan^(-1)x)dx=overset(1)underset(0)int((pi)/(2)-2tan^(-1)x) dx`
Intergrating a long y-axis, we get
`A=2overset(pi//4)underset(0)int x dy=2.overset(pi//4)underset(0)inttan y dy=[ log (secy )]_(0)^(pi//4)`
`=log sqrt(2)` sq. units
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