Question

Calculate the area bounded by the curve $y(y-1)$ and the y-axis ?

Answer 1

Equation of curve is given as

$y(y-1)=x$

It cuts the y-axis when $x=0$

so, $y=0,1$

To find the area , we will integrate it with respect to y from $0$ to $1$

so area $={\int }_0^{1}y(y-1)dy={\int }_0^1(y^2-y)dy={\left[\frac{y^3}{3}\right]}_0^1-{\left[\frac{y^2}{2}\right]}_0^1=\frac{1}{6}sq.unit$