Consider the following curve in polar coordinates: r = 2 − 2 sin θ. Which one of the following is the area enclosed by the curve for 0 ≤ θ ≤ 2π?

Question

Accepted Answer

The correct answer is D, 6π. GATE 2026 official key: (D). Area enclosed by a polar curve is A = ½∫₀^{2π} r² dθ. With r=2(1−sinθ), r²=4(1−2sinθ+sin²θ); since ∫sinθdθ=0 and ∫sin²θdθ=π over a full period, A = 2(2π−0+π) = 6π.