Area bounded by `y=sec^-1x`,`y=cot^-1x` and line x=1 is given by

Options

A. `log(3+2sqrt(2))-(pi)/(2)` sq. units
B. `(pi)/(2)-log (3+2sqrt(2))` sq. units
C. `pi-log_(e)3` sq. units
D. None of these

Answer

A

Explanation

Integrating along x-axis, we get
`A=overset(sqrt(2))underset(1)int(cosec ^(-1)x-sec^(-1)x) dx`
Integrating along y-axis, we get
`A=2overset(pi//6)underset(0)int(sec y-1)dy`
`=2[ log |sec y + tan y|-y]_(0)^(pi//4)`
`=2[log |sqrt(2)+1|-(pi)/(2)]`
`=log (3+2sqrt(2))-(pi)/(2)` sq. units.