Discussion
The area enclosed by the circle \( r = 2 \) is
Answer: D
Apply the polar formula over a complete revolution:
\[ A \;=\; \frac{1}{2}\int_{0}^{2\pi} 2^{2}\,d\theta \;=\; \frac{1}{2}(4)(2\pi) \;=\; 4\pi. \]
This agrees with \( \pi r^{2} = \pi(4) \). Dropping the half would give \( 8\pi \), and omitting the square would give \( 2\pi \), which is the circumference instead
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