Definite Integration Question 198
Question: The area enclosed between the curves $ y=ax^{2} $ and $ x=ay^{2}(a>0) $ is 1 sq. unit, then the value of a is
Options:
A) $ \frac{1}{\sqrt{3}} $
B) $ \frac{1}{2} $
C) 1
D) $ \frac{1}{3} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ y=ax^{2}\And x=ay^{2} $ Points of intersection are O (0, 0) & $ A( \frac{1}{a},\frac{1}{a} ) $
$ \therefore Area=\int\limits_0^{1/a}{( \sqrt{\frac{x}{a}}-ax^{2} )dx} $
$ =\frac{2}{3a^{2}}-\frac{1}{3a^{2}}=\frac{1}{3a^{2}}=1\Rightarrow a=\frac{1}{\sqrt{3}} $
BETA
