Question
Find the area enclosed between the curve y = β(25 β
xΒ²) and the x-axis in the first quadrant.Solution
We are given the curve: y = β(25 β xΒ²) This is the upper half of a circle with equation: xΒ² + yΒ² = 25
β 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 = ΟrΒ² = Ο Γ 25 = 25Ο So, area in the first quadrant = (1/4) Γ 25Ο = 25Ο / 4
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