Question

Maximum area of rectangle whose two sides are $x=x_0,x=\pi -x_0$ and which is inscribed in a region bounded by $y=\sin x$ and $x-$axis is obtained, when $x_0\in$

Answer 1

$A=$Area$=\sin x_0(\pi -2x_0),$
Area is maximum, if $\sin x_0=\pi -2x_0$
$\Rightarrow 0<\pi -2x_0<1$
$\Rightarrow \frac{\pi -1}{2}<x_0<\frac{\pi }{2}$
$\therefore x_0\in (\frac{\pi -1}{2},\frac{\pi }{2})$