The area bounded by the curve defined by \( x=2\cos\theta \) and \( y=3\sin\theta \) ; is
[where \( \theta \) is a parameter]
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 6\pi \) sq. units
Since \( \cos^2\theta+\sin^2\theta=1 \), eliminating \( \theta \) gives
\( \displaystyle \frac{x^2}{4}+\frac{y^2}{9}=1 \)
This is an ellipse with semi-axes a = 2 and b = 3. Its area is
\( \displaystyle \pi ab=\pi\times 2\times 3 \)
\( \displaystyle =6\pi\ \text{sq. units} \)
NCERT Exemplar:
Application of Integrals
