JEE Main Maths · Integrals

Even and Odd Functions

Even and Odd Functions (Integrals) was asked 3 times in 3 JEE Main shifts, 2021–2026, out of the 42 shifts Lumi analysed. 1 of the 3 had a numerical answer.

Times asked: 3; in 3 shifts
Years: 2021–2026
Usual format: Single correct; Multi-step
Pattern: Frequent; repeats across shifts

How it is asked

Integrate rational function then evaluate logs
Evaluate integral functions with even integrand

Difficulty

Easy 0Medium 1Hard 2

Where it sits

Chapter: Integrals. Topic: Definite Integral Properties, 30 questions over 12 ideas.

All 3 questions

Newest first, each with its options and official answer.

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
18 Mar 2021, Shift 1 · Q82Let $f(x)$ 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…HardNumerical value