Question

Interation of 0 to pai/2 root cos x

Answer 1

Step-by-step explanation:

We have,

$\int _{0 }^{ \frac{\pi}{2} } \sqrt{ \cos(x) } dx$

$= \int _{0} ^{ \frac{\pi}{2} } \frac{ \cos(x) }{ \sqrt{ \cos(x) } }dx$

$= \int _{0} ^{ \frac{\pi}{2} } \frac{ \cos(x) }{ \sqrt{1 - \sin ^{2} (x) } } dx$

$let \: \: \sin(x) = t \\ = > \cos(x) dx = dt$

$= \int _{0} ^{ 1 } \frac{dt}{ \sqrt{1 - {t}^{2} } }$

$= [ \sin^{ - 1} (t) ] _{0}^{1}$

$= [ \sin^{ - 1} ( \sin(x) ) ] _{0}^{1}$

$= [ x] _{0}^{1}$

$= 1$