Question

The area bounded by the parabola $y^2=x$, straight line $y=4$ and $y$-axis is square units is

• A. $\frac{16}{3}$ sq. unit
• B. $\frac{64}{3}$ sq. unit
• C. $7\sqrt{2}$ sq. unit
• D. None of these

Answer 1

Answer: (B)

$\frac{64}{3}$ sq. unit

Line $y=4$ meets the parabola $y^2=x$ at $A$
$\therefore 16=x$ and $A$ is $(16,4)$
$\therefore$ Required area
$={\int }_0^{4}xdy$
$={\int }_0^4{y}^{2}dy$
$=[y^3/3{]}_0^4$
$=\frac{64}{3}$sq units