Question

Area bounded by the curve $ay=3(a^2-x^2)$ and the x-axis is (in sq. units)

• A. $a^2$
• B. $2a^2$
• C. $3a^2$
• D. $4a^2$

Answer 1

Answer: (D)

$4a^2$

The parabola meets x-axis at the points, where
$\frac{3}{a}(a^2-x^2)=0\Rightarrow x\pm a$
So 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. units.