Question

19. The area bounded by the y-axis, y- cos x and y - sin x when 0xis(A) 2(V2-1) (B) 2-1(C) 2(D) /2

Answer 1

The equations are given as,

y=cosx and y=sinx

The graph formed by these two equations is given below,

The required area will be,

Required area=area( ABLA )+area( OBLO ) = ∫ 1 2 1 xdy + ∫ 1 1 2 xdy = ∫ 1 2 1 cos −1 ydy + ∫ 1 1 2 sin −1 ydy = [ y cos −1 y− 1− y 2 ] 1 2 1 + [ y sin −1 y− 1− y 2 ] 0 1 2

Simplify further,

area=[ cos −1 ( 1 )− 1 2 cos −1 ( 1 2 )+ 1− 1 2 ]+[ 1 2 sin −1 ( 1 2 )+ 1− 1 2 −1 ] = −π 4 2 + 1 2 + π 4 2 + 1 2 −1 = 2 2 −1 = 2 −1 square units

Therefore, the correct option is (B).