JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 18 March 2021, Shift 1, Maths Q82

Question 82 of 90 in this shift, Maths question 22 of 30, Section B.

Let

f(x)

and

g(x)

be two functions satisfying

f(x^2)+g(4-x)=4x^3

and

g(4-x)+g(x)=0

, then the value of

\int_{-4}^{4}f(x^2)\,dx

is __________.

Official answer

512

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Even and Odd Functions

Same idea in other shifts

Asked 3× in all

6 Apr 2026, Shift 2 · Q20The value of the integral $\int_{-1}^{1}\left(\frac{x^3+|x|+1}{x^2+2|x|+1}\right)dx$ is equal to :MediumSingle correct
31 Jan 2024, Shift 2 · Q12Let $f,g:(0,\infty)\to\mathbb{R}$ be two functions defined by $f(x)=\int_{-x}^{x}\left(|t|-t^2\right)e^{-t^2}dt$ and…HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.