Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main20198 Apr 2019Morning ShiftMathematicsArea Under CurvesActual

The area (in sq. units) of the region A = x , y ∈ R × R 0 ≤ x ≤ 3 , 0 ≤ y ≤ 4 , y ≤ x 2 + 3 x is

Options

  1. A26 3
  2. B8
  3. C53 6
  4. D59 6

Correct answer

D. 59 6

Step-by-step solution

The area of the region O C D is = ∫ 0 1 4 - x 2 + 3 x d x = 4 x - x 3 3 - 3 x 2 2 0 1 = 4 - 1 3 - 3 2 = 13 6 So, the area of the given region O A B C is = Area of O A B D - Area of O C D = 3 × 4 - 13 6 = 59 6

Practice Area Under Curves on Quantrex Academy →

More from Area Under Curves

Passage: Consider the curve C₁ given by y = e^ -x for x [0, 10 ] , and the curve C₂ given by y = e^ -x ( x + x) for x [0, 10 ] . Let n be the total number of points of intersection 2026Passage: Consider the ellipses given by x^2 + 4y^2 = 1 and 4x^2 + y^2 = 1 . Question: If is the area of the common region that lies inside both the given ellipses, then the value o 2026The area of the region (x, y) : x^2 - 8x y -x is : 2026The area of the region (x, y) : 0 y 6 - x, y^2 4x - 3, x 0 is: 2026The area of the region R = (x, y): xy 27, 1 y x^2 is equal to: 2026The area of the region bounded by the curves x+3y^2=0 and x+4y^2=1 is equal to: 2026The area of the region (x, y): y - |x|, y |x x|, y 0 is: 2026If the area of the region bounded by 16x^2 - 9y^2 = 144 and 8x - 3y = 24 is A, then 3(A + 6 _e(3)) is equal to _______. 2026 Full Area Under Curves list All JEE Main PYQs