JEE Main 2020MathematicsDefinite IntegrationHardMCQ

JEE Main 2020 — Definite Integration Question with Solution

JEE Main 2020 (04 Sep Shift 1)

Question

Let fx=x-2 and gx=ffx, x∈0,4. Then ∫03gx-fx dx is equal to

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Show full solutionCorrect option: A
Correct answer
A1

Step-by-step explanation

fx=x−2=2−x;    x<2x−2;     x≥2

gx=ffx=2−fx;    fx<2fx−2;     fx≥2

=2−2−x;      2−x<2,    x<22−x−2;      2−x≥2,    x<22−x−2;      x−2<2,    x≥2x−2−2;      x−2≥2,    x≥2

=2−2−x;     0<x<22−x−2;    x<02−x−2;     2≤x<4x−2−2;   x≥4

∫03gx−fxdx=∫02xdx+∫234−xdx−∫03x−2dx

=x2202+4x-x2223-2x-x2202-x22-2x23

=1.

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About this question

This is a previous-year question from JEE Main 2020, covering the Definite Integration chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.