Evaluate the following integrals: (1-35) `int_0^(pi//2)(asinx+bcosx)/(sinx+cosx)dx`

Explanation

Given,

I=`int_0^(pi//2)(asinx+bcosx)/(sinx+cosx)dx`...(1)

Using `int_a^bf(x)dx=int _a^bf(a+b-x)dx`

I=
`int_0^(pi//2)(acosx+bsinx)/(sinx+cosx)dx`...(2)

Adding (1) and (2) we get

`2I=(a+b)pi/2`

...