Evaluate the following integral: `int_0^(pi//2)(sintheta)/(sqrt(1+costheta))d theta`

Explanation

Given,`int_0^(pi//2)(sintheta)/(sqrt(1+costheta))d theta....(1)`

Let us assume `1 + cosθ = y `

Differentiating w.r.t `theta` on both sides we get,

` sinthetad theta = -dy……(2)`

Upper limit for the Definite Integral`theta=pi/2 ,y=1`

Lower limit for the Definite Integral:

⇒` theta = 0 ,y = 2……(4) `
Substituting (2),(3),(4) in the eq(1), we get,

`I=int _2^1 -dy/sqrt(y)`

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