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MHT CET202615 April 2026Morning ShiftMathematicsArea Under CurvesActual

If the area bounded by the curve x^2 = by and the lines y = 1, y = 4 in the first quadrant is 28 sq. units, then the value of b is...

Options

  1. A36
  2. B6
  3. C9
  4. D3

Correct answer

A. 36

Step-by-step solution

The equation of the curve is x^2 = by . In the first quadrant, x = b y . The area bounded by the curve and the lines y = 1 and y = 4 in the first quadrant is given by: ₁⁴ x , dy = 28 ₁⁴ b y , dy = 28 b [ 2 3 y^ 3/2 ]₁⁴ = 28 2 3 b (4^ 3/2 - 1^ 3/2 ) = 28 2 3 b (8 - 1) = 28 14 3 b = 28 b = 28 3 14 b = 6 b = 36 Answer: 36

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