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      Question

      Find the area enclosed between the curve y = √(25 –

      xΒ²) and the x-axis in the first quadrant.
      A (25Ο€)/16 Correct Answer Incorrect Answer
      B (25Ο€)/4 Correct Answer Incorrect Answer
      C (25 Ο€)/2 Correct Answer Incorrect Answer
      D (25Ο€)/8 Correct Answer Incorrect Answer

      Solution

      We are given the curve: y = √(25 – 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 = Ο€rΒ² = Ο€ Γ— 25 = 25Ο€ So, area in the first quadrant = (1/4) Γ— 25Ο€ = 25Ο€ / 4

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