Draw a vertical line say $x=t$ on curve $y= \sqrt{x}$ between $x=0$ and $x=a$ such that area under the curve from $x=0$ to $x=t$ equals area under the curve from $x=t$ to $x=a$.
I am looking for a generalized approach for other functions such as $y = \ln(x)$
Best Answer
Hint
Find $t \in (0,a)$ such that
$$\int_0^t \sqrt x dx = \frac{1}{2} \int_0^a \sqrt x dx.$$