Find the area bounded by the y-axis, `y=cosx ,a n dy=sinxw h e n0lt=xlt=pi/2dot`

Options

A. `2(sqrt(2-1))`
B. `sqrt(2)-1`
C. `sqrt(2)+1`
D. `sqrt(2)`

Answer

B

Explanation

Given curves `y=sin x ` and `y-cos x` meet
wher `sin x= cos x`
and `tan x=1`
`implies x=(pi)/(4)`

` :. ` Area of required shaded region
`=int_(0)^(pi//2)(cos x-sin x)dx=[sin x+cos x]_(0)^(pi//4)`
`="sin"(pi)/(4)+"cos"(pi)/(4)-(0+1)=(1)/(sqrt(2))+(1)/(sqrt(2))-1`
`=(2)/(sqrt(2))-1=sqrt(2)-1` sq. units.