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The area bounded by the curves y=cosx an...

The area bounded by the curves `y=cosx` and `y=sinx` between the ordinates `x=0` and `x=(3pi)/2` is

A

`4sqrt2-1`

B

`4sqrt2+1`

C

`4sqrt2-2`

D

`4sqrt2+2`

Text Solution

Verified by Experts

The correct Answer is:
C
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`
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