Question

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

• A. $7$
• B. $\frac{7}{2}$
• C. $\frac{7}{3}$
• D. $\frac{7}{4}$

Answer 1

Answer: (C)

$\frac{7}{3}$

Area $\Rightarrow {\int }_1^4\frac{\sqrt{y}}{2}dy$

$=\frac{1}{2}1\frac{[y^{3/2{]}^4}}{3}$

$=\frac{1}{3}[4^{3/2}-1]=\frac{1}{3}(2^{2\times \frac{3}{2}}-1)$

$=\frac{7}{3}$