Question

The value of the integral ${\int }_0^{\frac{{\pi }^2}{4}}\sin \sqrt{x}dx$ is

• A. $1$
• B. $1/2$
• C. $3/2$
• D. none of these

Answer 1

The correct option is D none of these

Let $I={\int }_0^{\frac{{\pi }^2}{4}}\sin \sqrt{x}dx$
Substitute $\sqrt{x}=t$

$\Rightarrow \frac{1}{2}\frac{1}{\sqrt{x}}dx=dt$
$I=2{\int }_0^{\frac{\pi }{2}}t\sin tdt=2$