Definite Integration Question 141
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:
Options:
A) 7/9
B) 14/3
C) 7/3
D) 14/9
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Required area $ =\int\limits _{y=1}^{4}{\sqrt{\frac{y}{9}}dy=\frac{1}{3}\int\limits _{y=1}^{4}{{y^{1/2}}}dy} $
$ =\frac{1}{3}\times \frac{2}{3}| ({y^{3/2}}) |_1^{4}=\frac{2}{9}[{{({4^{1/2}})}^{3}}-{{({1^{1/2}})}^{3}}] $
$ =\frac{14}{9} $ sq. units.
BETA
