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MHT CET202525 Apr 2025Morning ShiftMathematicsArea Under CurvesActual

The area bounded by the parabolas y =9 x^2, y = x^2 16 and the line y =1 is

Options

  1. A22 9 sq. units
  2. B44 9 sq. units
  3. C8 9 sq. units
  4. D26 9 sq. units

Correct answer

B. 44 9 sq. units

Step-by-step solution

Given the parabolas y = 9x^2 and y = x^2 16 and the line y = 1 , the area is determined by integrating with respect to y due to the symmetry about the y -axis. Solving for x in terms of y yields the right boundary x = 4 y from y = x^2 16 and the left boundary x = y 3 from y = 9x^2 in the first quadrant. The integral for half the area is A_ half = ₀^1 ( 4 y - y 3 ) dy = 11 3 ₀^1 y dy . ₀^1 y^ 1/2 dy = [ 2 3 y^ 3/2 ]₀^1 = 2 3 Thus, A_ half = 11 3 2 3 = 22 9 . Due to symmetry, the total area is 2 22 9 = 44 9 square un

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