PrepRung
Sign inSign up free

JEE Main 2021 · Mathematics · Area Under Curves · medium

The total area of the region enclosed between the curves y=x^3 and y=x is

Single correct option

The total area of the region enclosed between the curves y=x3y=x^3 and y=xy=x is
  1. A. 14\dfrac14
  2. B. 12\dfrac12
  3. C. 11
  4. D. 13\dfrac13
Show answer and solution

Answer: (B) 12\dfrac12

Solving x3=xx^3=x gives x=−1,0,1x=-1,0,1. By symmetry about the origin the two lobes are equal. On [0,1][0,1] the line is above the cubic, so one lobe is int01(x−x3),dx=tfrac12−tfrac14=tfrac14\\int_0^1(x-x^3)\\,dx=\\tfrac12-\\tfrac14=\\tfrac14. The total area is 2timestfrac14=tfrac122\\times\\tfrac14=\\tfrac12. The value tfrac14\\tfrac14 counts only one lobe, a common slip.
Report a mistake

Original question written in the JEE Main 2021 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake