Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main20249 Apr 2024Evening ShiftMathematicsArea Under CurvesActual

The area (in square units) of the region enclosed by the ellipse x^2+3 y^2=18 in the first quadrant below the line y=x is

Options

  1. A3 - 3 4
  2. B3 +1
  3. C3
  4. D3 + 3 4

Correct answer

C. 3

Step-by-step solution

x^2 18 + y^2 6 =1 aligned & x^2 18 + 3 x^2 18 =1 4 x^2=18 x^2= 9 2 & _ 3 2 ^ [3] 2 18-x^2 3 d x & = 1 3 ( x 18-x^2 2 + 18 2 ⁻¹ x 3 2 )_ 3 2 ^ 3 2 & = 1 3 (9 2 - 3 2 2 3 3 2 -9 6 ) aligned Required Area aligned & = 1 2 9 2 + ( 18 6 - 9 3 4 ) 1 3 & = 3 aligned

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