Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202525 Apr 2025Evening ShiftMathematicsArea Under CurvesActual

The area bounded by the curve y =4 x-x^2 and X - axis in square units, is

Options

  1. A32 3
  2. B16
  3. C32
  4. D21 1 3

Correct answer

A. 32 3

Step-by-step solution

The area bounded by y = 4x - x^2 and the X-axis is determined by finding the points of intersection. Setting y = 0 yields 4x - x^2 = 0 or x(4 - x) = 0 , so x = 0 and x = 4 serve as the limits of integration. Between these limits, the parabola is above the X-axis since y is positive. The area is thus given by the definite integral ₀⁴ (4x - x^2) dx . Evaluating the integral: [ 2x^2 - x^3 3 ]₀⁴ = (32 - 64 3 ) - 0 = 32 3 . This matches option A. Answer: A

Practice Area Under Curves on Quantrex Academy →

More from Area Under Curves

Find the area bounded by the curve y = |2 - x| , the x –axis, and the lines x = 0 and x = 5 2026The area enclosed by the curve y = -x^2 and the line x + y + 2 = 0 is 2026The area of the region bounded by the line y = x + 2 and the curve x = -y^2 is 2026The area of the region in the first quadrant enclosed by the x -axis, the line x = 3 ,y and the circle x^2 + y^2 = 4 is 2026The area of the region bounded by the curve y^2 = x^3 , the y -axis and the lines y = 1 and y = 8 is 2026The area enclosed by the curve x = 3 , y = 3 is 2026The area in square units of the region bounded by the curve y = 16 - x^2 and lines x = 0, x = 4 above the X-axis is 2026The area bounded by the curves y = |x| - 1 and y = -|x| + 1 is 2026 Full Area Under Curves list All MHT CET PYQs