Definite Integration Question 305
Question: The volume of the solid generated by revolving about the y-axis the bounded by the parabola $ y=x^{2} $ and $ x=y^{2} $ is
[UPSEAT 2002]
Options:
A) $ \frac{21}{5}\pi $
B) $ \frac{24}{5}\pi $
C) $ \frac{2}{15}\pi $
D) $ \frac{5}{24}\pi $
Show Answer
Answer:
Correct Answer: C
Solution:
$ V=\int_0^{1}{\pi x^{2}dy} $
$ =\pi \int_0^{1}{(y^{4}-y^{2})dy} $
$ =\pi [ \frac{y^{5}}{5}-\frac{y^{3}}{3} ]_0^{1} $
$ =\pi [ \frac{1}{5}-\frac{1}{3} ] $
$ =\frac{-2\pi }{15} $ i.e., $ \frac{2\pi }{15} $ , (Volume should be positive).
BETA
