Question

If $y={\int }_0^x\sqrt{\sin x}dx$, then the value of $\frac{dy}{dx}$ at $x=\frac{\pi }{2}$, is

• A. $0$
• B. $1$
• C. $-1$
• D. none of these

Answer 1

Answer: (B)

$1$

$y={\int }_0^x\sqrt{\sin x}dx$
Using leibnitz theorem, differentiating both sides,
$\frac{dy}{dx}=\sqrt{\sin x}-0\Rightarrow \frac{dy}{dx}=\sqrt{\sin x}$
For $x=\frac{\pi }{2}$, we get

$\frac{dy}{dx}=\sqrt{\sin \frac{\pi }{2}}=1$