Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Application of Integrals

Question:
The area enclosed by the curve \(x=a\cos t,y=a\sin t, t\in [0,2\pi]\) is
Options:
\(2a\pi\)
\(\frac{\pi}{2}a^{2}\)
\(\pi a\)
\(\frac{\pi}{4}a^{2}\)
Correct Answer:
\(\pi a\)
Explanation:
\(\begin{aligned}\text{Area}&=\frac{1}{2}\int_{0}^{2\pi}\left(x\frac{dy}{dt}-y\frac{dx}{dt}\right)dt\\ &=\pi a\end{aligned}\)