Hi Everyone,

Please help me with this integration:

$\displaystyle \int_0^\pi {\sqrt {2 + 2\sin (x)} } dx$

This is what I've tried so far:

when I substitute

$\displaystyle z = 1 + \sin (x)$

and

$\displaystyle x \to \pi ,z \to 1$

$\displaystyle x \to 0,z \to 1$

I got:

$\displaystyle \sqrt 2\int_1^1 {\frac{1}{{\sqrt {2 - z} }}dz} $

the new boundaries is my main problem here, it will give me a value of 0.

However, when I check my answer, it should be

$\displaystyle 4\sqrt 2 $