Question

Evaluate : ${\int }_0^a\frac{1}{\sqrt{a^2-x^2}}dx.$

Answer 1

Now,

${\int }_0^a\frac{1}{\sqrt{a^2-x^2}}dx.$

$={\left[{\sin }^{-1}\frac{x}{a}\right]}_0^a$

$=(\frac{\pi }{2}-0)$

$=\frac{\pi }{2}$.