The area bounded by `y = sin^(-1)x,x=(1)/(sqrt(2))` and X-axis is

Options

A. `((1)/(sqrt(2))+1)`sq unit
B. `(1-(1)/(sqrt(2)))`sq unit
C. `(pi)/(4sqrt(2))` sq unit
D. `((pi)/(4sqrt(2))+{(1)/(sqrt(2))-1})` sq unit

Answer

D

Explanation

Required area = Area of rectangular OABC - Area of curve OABO
`=(pi)/(4sqrt(2))-int_(0)^(pi//4) sin y dy`
`=(4)/(4sqrt(2))+[cos y]_(0)^(pi//4)`
`=[ (pi)/(4sqrt(2))+{(1)/(sqrt(2))-1}]` sq unit