Definite Integration Question 294

Question: The area between the parabola $ y^{2}=4ax $ and $ x^{2}=8ay $ is

[RPET 1997]

Options:

A) $ \frac{8}{3}a^{2} $

B) $ \frac{4}{3}a^{2} $

C) $ \frac{32}{3}a^{2} $

D) $ \frac{16}{3}a^{2} $

Show Answer

Answer:

Correct Answer: C

Solution:

Required area $ A=\int_0^{(a{2^{8/3}})}{\sqrt{4ax}}dx-\int_0^{a{2^{8/3}}}{\frac{x^{2}}{8a}}dx=\frac{32a^{2}}{3} $