Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202415 May 2024Evening ShiftMathematicsArea Under CurvesActual

The area enclosed between the parabola y^2=4 x and the line y=2 x-4 is

Options

  1. A17 3 sq. units
  2. B15 sq. units
  3. C19 3 sq. units
  4. D9 sq. units

Correct answer

D. 9 sq. units

Step-by-step solution

Putting x= y^2 4 in y=2 x-4 , we get aligned & y=2 ( y^2 4 )-4 & y^2-2 y-8=0 & (y-4)(y+2)=0 & y=4,-2 aligned aligned & Required area = _ -2 ^4 ( y+4 2 - y^2 4 ) d y & = 1 2 [ y^2 2 +4 y ]_ -2 ^4- 1 4 [ y^3 3 ]_ -2 ^4 & = 1 2 [8+16-(2-8)]- 1 12 [64-(-8)] & =15-6 & =9 sq. units aligned

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