The area bounded by `y=sec^(-1)x , y=cos e c^(-1)x ,` and line `x-1=0` is `log(3+2sqrt(2))-pi/2s qdotu n i t s` `"pi"/2-log(3+2sqrt(2))s qdotu n i t s` `pi-(log)_e3s qdotu n i t s` None of these

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.