Definite Integration Question 196
Question: Area enclosed by the parabola $ ay=3(a^{2}-x^{2}) $ and x-axis is
Options:
A) $ 4a^{2} $ sq. unit
B) $ 12a^{2} $ sq. unit
C) $ 4a^{3} $ sq. unit
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
The parabola meets x-axis at the points, where $ \frac{3}{a}(a^{2}-x^{2})=0\Rightarrow x=\pm a. $ So the required area $ =\int _{-a}^{a}{\frac{3}{a}(a^{2}-x^{2})dx=\frac{6}{a}\int_0^{a}{(a^{2}-x^{2})dx=4a^{2}}} $ sq. unit.
BETA
