Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202617 April 2026Morning ShiftMathematicsArea Under CurvesActual

Area enclosed by curve y = 2x^2 and lines x 1, y 4 is ..... sq. units

Options

  1. A8 2 -10 3
  2. B8( 2 -1) 3
  3. C4 2 -5 3
  4. D4( 2 -1) 3

Correct answer

A. 8 2 -10 3

Step-by-step solution

The region is bounded by the curve y = 2x^2 , the vertical line x = 1 , and the horizontal line y = 4 . The intersection of y = 2x^2 and y = 4 in the region x 1 is given by: 2x^2 = 4 x^2 = 2 x = 2 The required area A is the integral of the upper boundary minus the lower boundary from x = 1 to x = 2 : A = ₁^ 2 (4 - 2x^2) dx A = [ 4x - 2x^3 3 ]₁^ 2 A = ( 4 2 - 4 2 3 ) - ( 4 - 2 3 ) A = 8 2 3 - 10 3 = 8 2 - 10 3 Answer: 8 2 -10 3

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