The area bounded by the curves y=cos x and y= sin x between the ordinates x=0 and `x=3pi//2` is

Options

A. `4sqrt2-1`
B. `4sqrt2+1`
C. `4sqrt2-2`
D. `4sqrt2+2`

Answer

C

Explanation

Required area A is given by
`A underset(0)overset(3pi//2)(int)|cosx-sinx|dx`

`impliesA=underset(0)overset(pi//4)(int)|cosx-sinx|dx+underset(pi//4)overset(5pi//4)(int)|cosx-sinx|dx+underset(5pi//4)overset(3pi//2)(int)|cosx-sinx""|dx`
`impliesA=underset(0)overset(pi//4)(int)(cosx-sinx)dx+underset(pi//4)overset(5pi//4)(int)(sinx-cosx)dx+underset(5pi//4)overset(3pi//2)(int)(cosx-sinx)dx`
`impliesA=[sinx+cosx]_(0)^(pi//4)+[-cosx-sinx]_(pi//4)^(5pi//4)+[sinx+cosx]_(5pi//4)^(3pi//2)`
`impliesA=(sqrt2-1)+(sqrt2+sqrt2)+(-1+sqrt2)=4sqrt2-2`