Question

ans please integration by substitution ​

Answer 1

Answer:

$\int \sqrt{ \cos(x) } \sin { }^{3} (x) dx \\ \\ = \int \sqrt{ \cos(x) } \sin { }^{2} x. \sin(x) dx \\ \\ = \int \sqrt{ \cos(x) } (1 - \cos{ }^{2} (x) ) \sin(x) dx \\ \\ put \: \: y = \cos(x) \implies \: sin \: xdx = dy \\ limits \: \: \cos(0) \: \: to \: \: cos \frac{\pi}{2} \: \: or \: \: 1 \: \: to \: \: 0 \\ \\ \int \: \sqrt{y} (1 - {y}^{2} )dy \\ \\ = \int \: ( {y}^{1 \over2} - {y}^{5 \over2} )dy \\ \\ = ( \frac{2}{3} - \frac{2}{7} ) \\ \\ = \frac{8}{20}$