Question

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

• A. $\frac{16}{3}$
• B. $7\sqrt{2}$
• C. $\frac{32}{3}$
• D. $\frac{64}{3}$

Answer 1

The correct option is D $\frac{64}{3}$

R.E.F image

Taking a rectangle of width

dy and length as x-coordinate

of parabola, Area would be,

$A{=}^4{\int }_{0}xdy{=}^4{\int }_0{y}^{2}dy={\left[\frac{y^3}{3}\right]}_4^0$

$=\frac{64}{3}\Rightarrow \left(D\right)$