Question

The area bounded by the curve $y={\sin }^{-1}x$ and the lines $x=0,|y|=\frac{\pi }{2}$ is

Answer 1

$y={\sin }^{-1}x\Rightarrow x=\sin y$
The required area $=2\underset{0}{\overset{\frac{\pi }{2}}{\int }}xdy$
$=2\underset{0}{\overset{\frac{\pi }{2}}{\int }}\sin ydy=-2[\cos y{]}_0^{\frac{\pi }{2}}=2$ Sq.unit