If $y=\int_0^x\sqrt{\sin x}dx$ the value of $\frac{dy}{dx}$ at $x=\frac{\pi}{2}$ is:

0 1 -1 None of these

1

$\frac{dy}{dx}=\frac{d}{dx}[\int\limits_0^x\sqrt{\sin x\,dx}]=\sqrt{\sin x}⇒\frac{dy}{dx}|_{x=π/2}=\sqrt{\sin π/2}=1$