The area of the region bounded by the ellipse $\frac{x^2}{4} + \frac{y…

Question

The area of the region bounded by the ellipse $\frac{x^2}{4} + \frac{y^2}{9} = 1$ is

Accepted Answer

D. $6\pi$

1. Here $a^2 = 4$ and $b^2 = 9$, so $a = 2$ and $b = 3$.
2. Area of an ellipse $= \pi a b = \pi \cdot 2 \cdot 3$.
3. Therefore $A = 6\pi$. (Multiplying $a^2 b^2 = 36$ wrongly gives $36\pi$.)
_Source: syllabus Mathematics Ch 8 "Application of Integrals", p.4_

Answer

$36\pi$

Answer

$5\pi$

Answer

$12\pi$

The area of the region bounded by the ellipse $\frac{x^2}{4} + \frac{y^2}{9} = 1$ is

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