Question

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