Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202521 Apr 2025Morning ShiftMathematicsArea Under CurvesActual

The area inside the parabola y^2=4 a x , between the lines x=a and x=4 a is equal to

Options

  1. A4 a^2 sq. units
  2. B8 a^2 sq. units
  3. C56 a^2 3 sq. units
  4. D35 a^2 3 sq. units

Correct answer

C. 56 a^2 3 sq. units

Step-by-step solution

Area inside the parabola y^2 = 4ax between x = a and x = 4a . The parabola y^2 = 4ax is symmetric about the x-axis, with the upper half given by y = 2 ax . The total area is twice the area above the x-axis, so we compute A = 2 _a^ 4a 2 ax dx = 4 a _a^ 4a x dx . Evaluating the integral: 4 a [ 2 3 x^ 3/2 ]_a^ 4a = 8 a 3 ( (4a)^ 3/2 - a^ 3/2 ) . Simplifying: (4a)^ 3/2 = 8a^ 3/2 , so A = 8 a 3 (8a^ 3/2 - a^ 3/2 ) = 8 a 3 7a^ 3/2 = 56 3 a^2 . This corresponds to option C : 56a^2 3 square units.

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