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## Homework Statement

I need to calculate [tex]\int_0^{2\pi} \sqrt{1-\sin{x}}\, dx[/tex] when I compute the indefinite integral I get [tex]2\sqrt{\sin{x}+1}+C[/tex] but when I evaluate it into the integration limits it turns out to be 0 wich doesn't make sence since the original function is clearly positive...I already tested this result in wolfram alpha and my calculation of the definite integral is perfect but when I tested the definite integral wolfram computed its value to be [tex]4\sqrt{2}[/tex]. I can't find out what's wrong with my procedure. Please help!

## Homework Equations

## The Attempt at a Solution

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