The solution for `x` of the equation `int_(sqrt(2))^x(dt)/(tsqrt(t^2-1))=pi/2` is `pi` (b) `(sqrt(3))/2` (c) `2sqrt(2)` (d) none of these

Options

A. `(sqrt(3))/(2)`
B. `2sqrt(2)`
C. 2
D. `-sqrt(2)`

Answer

D

Explanation

We have,
`overset(x)underset(sqrt(2))int(1)/(tsqrt(t^(2)-1))dt=(pi)/(2)`
`rArr[sec^(-1)]_(sqrt(2))^(x)=(pi)/(2)`
`rArrsec^(-1)x sec^(-1)sqrt(2)=(pi)/(2)`
`rArr sec^(-1)-(pi)/(4)=(pi)/(2)`
`rArrsec^(-1)x=((pi)/(4)+(pi)/(4))rArr=sec((pi)/(2)+(pi)/(4))=-cosec(pi)/(4)=-sqrt(2)`