Question
Find the area enclosed between the curve y = √(25 –
x²) and the x-axis in the first quadrant.Solution
We are given the curve: y = √(25 – x²) This is the upper half of a circle with equation: x² + y² = 25
⇒ a circle of radius 5, centered at the origin. We are asked to find the area enclosed between the curve and the x-axis in the first quadrant, i.e., one-fourth of the area of the full circle. Area of full circle = πr² = π × 25 = 25π So, area in the first quadrant = (1/4) × 25π = 25π / 4
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