Question

Solve:

$\int \sqrt{{\sin }^{4}x}dx$

Answer 1

Consider the given integral.

$I=\int \sqrt{{\sin }^{4}x}dx$

$I={\sin }^{2}xdx$

$I=\frac{1}{2}\int (1-\cos 2x)dx$

$I=\frac{1}{2}(x-\frac{\sin 2x}{2})+C$

Hence, this is the answer.