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 $\underset{y=1}{\overset{4}{\int }}$$\sqrt{\frac{y}{9}}dy$
$\frac{1}{3}$$\underset{y=1}{\overset{4}{\int }}$$y^{1/2}dy=\frac{1}{3}\times \frac{2}{3}\left(y^{3/2}\right){|}_1^4$
$=\frac{2}{9}\left[{\left(4^{1/2}\right)}^3-{\left(1^{1/2}\right)}^3\right]=\frac{2}{9}\left[8-1\right]$
$\frac{2}{9}\times 7=\frac{14}{9}$ sq. units.