JEE Main Maths · Integrals

Composite Function Substitution

Composite Function Substitution (Integrals) was asked 5 times in 4 JEE Main shifts, 2021–2025, out of the 42 shifts Lumi analysed. 1 of the 5 had a numerical answer.

Times asked: 5; in 4 shifts
Years: 2021–2025
Usual format: Single correct; Multi-step
Pattern: Comes in cycles; repeats across shifts

How it is asked

Indefinite integral with radical then evaluate constant
Integral of f' powers times f'' from tangent angles

Difficulty

Easy 0Medium 2Hard 3

Where it sits

Chapter: Integrals. Topic: Integration by Substitution, 22 questions over 15 ideas.

All 5 questions

Newest first, each with its options and official answer.

3 Apr 2025, Shift 1 · Q18Let $f(x) = \int x^3\sqrt{3 - x^2}\,dx$ . If $5f(\sqrt{2}) = -4$ , then $f(1)$ is equal toMediumSingle correct
30 Jan 2024, Shift 2 · Q12Let $y = f(x)$ be a thrice differentiable function in $(-5, 5)$ . Let the tangents to the curve $y = f(x)$ at $(1, f(1))$ and $(3, f(3))$ …HardSingle correct
30 Jan 2024, Shift 2 · Q13Let $f: \mathbb{R} \to \mathbb{R}$ be a function defined by $f(x) = \frac{x}{(1+x^4)^{1/4}}$ , and $g(x) = f(f(f(f(x))))$ . Then,…HardSingle correct
16 Mar 2021, Shift 2 · Q81For real numbers $\alpha,\beta,\gamma$ and $\delta$ , if…HardNumerical value
18 Mar 2021, Shift 1 · Q73The integral $\int\dfrac{(2x-1)\cos\sqrt{(2x-1)^2+5}}{\sqrt{4x^2-4x+6}}\,dx$ is equal to : (where c is a constant of integration)MediumSingle correct