GATE 2025 AE – Question 42
The equation of a closed curve in two-dimensional polar coordinates is given by $r = \frac{2}{\sqrt{\pi}}(1 - \sin\theta)$. The area enclosed by the curve is ________ (answer in integer).
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Correct answer: 6
Explanation
The area is $\frac{1}{2}\int_0^{2\pi}r^2d\theta = \frac{1}{2}\cdot\frac{4}{\pi}\int_0^{2\pi}(1 - 2\sin\theta + \sin^2\theta)d\theta = \frac{2}{\pi}(2\pi - 0 + \pi) = 6$.