Question

If ${\int }_0^{\pi /2}\sin x\cos xdx$ is equal to:

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $2$
• D. $1$

Answer 1

The correct option is A $\frac{1}{2}$

${\int }_0^{\pi /2}\sin x\cos xdx$

$\sin x=t⟹\cos xdx=dt$
$x\to 0\to \frac{\pi }{2}$
$t\to 0\to 1$

$\Rightarrow {\int }_0^{\pi /2}tdt$
$\Rightarrow {\frac{t^2}{2}|}_0^1$
$\Rightarrow \frac{1}{2}-0=\frac{1}{2}$