Question

Find the area bounded by the parabola $y^2=4x$ and the straight line y = x. (Draw the figure in answer book)

Answer 1

Intersection point of the curves $y^2=4x$ and $y=x$

are $(0,0)$ and $(1,2)$

Area of the the shaded region is given by:

$A={\int }_0^{2}y-\frac{y^2}{4}$

$\Rightarrow A={\left[\frac{y^2}{2}\right]}_0^2-{\left[\frac{y^3}{12}\right]}_0^2$

$\Rightarrow A=2-\frac{2}{3}=\frac{4}{3}sq.units$