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Evaluate the following integral: int0^(p...

Evaluate the following integral: `int_0^(pi//2)|sin x-cos x|dx`

Text Solution

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Given:`int_0^(pi/2)|sin x-cos x|dx`
`I=int_0^(pi/2)|sin x-cos x|dx`
`implies` here `f(x)=(sinx-cosx)`when `x>=0` or `f(x)=-(sinx-cosx)`when `x<0`
Then
`I=-int_0^(pi/4)(sin x-cos x)dx+int_(pi/4)^(pi/2)(sin x-cos x)dx`
`I=[-(-cosx-sinx)]_0^(pi/4)+[-cosx-sinx]_(pi/4)^(pi/2)`
`I=2sqrt2-2`
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