Question

The area bounded by the parabola $y=4x^2,x=0$ and $y=1,y=4$ is equal to

• A. $\frac{6}{3}$ Sq.units
• B. $\frac{7}{3}$ Sq.units
• C. $\frac{14}{3}$ Sq.units
• D. $\frac{5}{3}$ Sq.units

Answer 1

The correct option is C $\frac{14}{3}$ Sq.units


Given $y=4x^2$
$\Rightarrow x=\frac{\sqrt{y}}{2}$
Required area $=2\underset{1}{\overset{4}{\int }}\frac{1}{2}\sqrt{y}dy$
$=\frac{2}{3}{\left[y^{3/2}\right]}_1^4=\frac{14}{3}$ Sq.units