AktiraAktira JEE
Subscribe
MathsJEE Main 6 Apr 2026, Shift 1·Q20·MCQ·Moderate

Area under Curves · Area between curves

Let ee be the base of natural logarithm and let f:{1,2,3,4}→{1,e,e2,e3}andg:{1,e,e2,e3}→{1,12,13,14}f : \{1, 2, 3, 4\} \to \{1, e, e^2, e^3\} \quad\text{and}\quad g : \{1, e, e^2, e^3\} \to \left\{1, \dfrac12, \dfrac13, \dfrac14\right\} be two bijective functions such that ff is strictly decreasing and gg is strictly increasing. If ϕ(x)=[f−1{g−1(12)}]x,\phi(x) = \left[f^{-1}\left\{g^{-1}\left(\dfrac12\right)\right\}\right]^x, then the area of the region R={(x,y):x2≤y≤ϕ(x), 0≤x≤1}R = \{(x, y) : x^2 \le y \le \phi(x),\ 0 \le x \le 1\} is:
  1. (1)3−log⁡e(2)3log⁡e(2)\dfrac{3 - \log_e(2)}{3\log_e(2)}
  2. (2)13log⁡e(2)\dfrac{1}{3\log_e(2)}
  3. (3)3+log⁡e(2)3 + \log_e(2)
  4. (4)3+log⁡e(2)2+log⁡e(3)\dfrac{3 + \log_e(2)}{2 + \log_e(3)}

Video solution coming soon

We're animating every PYQ step by step. Subscribe to get them first.

Subscribe

See the full 6 Apr 2026, Shift 1 paper

More on Area between curves