Question

Evaluate $\int \sqrt{1-\sin 2x}dx$

Answer 1

We have,

$\int \sqrt{1-\sin 2x}dx$

$=\int \sqrt{{\sin }^{2}x+{\cos }^{2}x-2\sin x.\cos x}dx$

$=\int \sqrt{(\sin x-\cos x{)}^2}dx$

$=\int \sin xdx-\int \cos xdx$

$=-\cos x-\sin x+C$