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
$\int\limits_{0}^{2}\left(2 \sqrt{2} x^{1 / 2}-2 x\right) d x$
$=\left(\frac{4 \sqrt{2}}{3} x^{3 / 2}-x^{2}\right)_{0}^{2}=\frac{4}{3}$ sq. units