Question

The area of the region bounded by the curve $y^2=8x$ and the line $y=2x$ is

• A. $\frac{16}{3}$ sq.units
• B. $\frac{4}{3}$ sq.units
• C. $\frac{3}{4}$ sq.units
• D. $\frac{8}{3}$ sq.units

Answer 1

Answer: (B)

Solving $y^2=8x$ and $y=2x$, we get
$(x,y)=(0,0),(0,4)$

So, area bounded by the curve is
$\underset{0}{\overset{2}{\int }}\left(2\sqrt{2}{x}^{1/2}-2x\right)dx$
$={\left(\frac{4\sqrt{2}}{3}{x}^{3/2}-x^2\right)}_0^2=\frac{4}{3}$ sq. units