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Area Under the Curve
Area Under a Curve
Premium Question
Grade 12

Question:

The area of the region bounded by the curve $y = \sqrt{4 - x^2}$ and the $x$-axis is:
(1) $2\pi$
(2) $\pi$
(3) $4\pi$
(4) $\frac{\pi}{2}$

Step-by-Step Solution

Key Concept: Recognise $y = \sqrt{4 - x^2}$ as the upper half of a circle of radius 2, and use the known formula for the area of a semicircle rather than direct integration.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)

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