Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
99 Percentile Qs Bank for JEE MainMathematicsArea Under Curves

If a curve y= a x + b x passes through the point (1,2) and the area bounded by the curve, line x=4 and X -axis is 8 sq. units, then

Options

  1. Aa =3, ~b =-1
  2. Ba =3, ~b =1
  3. Ca =-3, ~b =1
  4. Da =-3, ~b =-1

Correct answer

A. a =3, ~b =-1

Step-by-step solution

The given curve passes through (1,2) . 2=a+b According to the given condition, ₀^4(a x +b x) d x=8 ...(i) 2 a 3 [x^ 3 / 2 ]₀^4+ b 2 [x^2 ]₀^4=8 2 a 3 8+8 ~b =8 2 a+3 b=3 ...(ii) From (i) and (ii), we get a =3, ~b =-1

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 99 Percentile Qs Bank for JEE Main PYQs