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COMEDK2024MathematicsArea Under CurvesActual

The area of the region (in sq units) bounded by the curve y= 16-x^2 and x -axis is

Options

  1. A256
  2. B16
  3. C20
  4. D8

Correct answer

D. 8

Step-by-step solution

The given equation is y = 16 - x^2 . Squaring both sides, we get y^2 = 16 - x^2 , which implies x^2 + y^2 = 16 . This is the equation of a circle centered at the origin (0, 0) with radius r = 16 = 4 . Since y = 16 - x^2 , y must be non-negative, meaning the curve represents the upper semi-circle. The area of a full circle is r^2 . For a circle with radius r = 4 , the area is (4)^2 = 16 . The area of the upper semi-circle bounded by the x -axis is half the area of the full circle, which is 1 2 16 = 8 . Answer: 8

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