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By using the properties of definite int...

By using the properties of definite integrals, evaluate the integrals`int_0^(pi/2) (sinx-cosx)/(1+sinxcosx)dx`

Text Solution

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Let `I=int_0^(pi/2) (sinx-cosx)/(1+sinxcosx)dx`
`=int_0^(pi/2) (sinx)/(1+sinxcosx)dx-int_0^(pi/2) (cosx)/(1+sinxcosx)dx`
Here `a+b-x=pi/2-x`, so using the property
`int_a^bf(x)dx=int_a^bf(a+b-x)dx`
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