Question

The area of the region (in sq. units), in the first quadrant bounded by the parabola $y = 9x^2$ and the lines $x=0, y=1$ and $y=4$, is:

• A. $7/9$
• B. $14/3$
• C. $7/3$
• D. $14/9$

Answer 1

Answer: (D)

Required area $\int\limits^{{4}}_{{y=1}}$$\sqrt{\frac{y}{9}}dy$
$\frac{1}{3}$$\int\limits^{{4}}_{{y=1}}$$y^{1/2}dy=\frac{1}{3}\times\frac{2}{3}\left(y^{3/2}\right)|^4_1$
$=\frac{2}{9}\left[\left(4^{1/2}\right)^{3}-\left(1^{1/2}\right)^{3}\right]=\frac{2}{9}\left[8-1\right]$
$\frac{2}{9}\times7=\frac{14}{9}$ sq. units.