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JEE Main Indefinite and Definite Integrals questions with solutions

Techniques of integration and properties of definite integrals. 16 questions from our 2016–2025 JEE Main pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Indefinite and Definite Integrals for JEE Advanced

JEE Main 2025

The value of ∫0^π/2(sin ^2x)/(sin x+cos x) dx isJEE Main 2025 · hard
The value of ∫0^4 x lfloor xrfloor dx, where lfloor xrfloor denotes the greatest integer not exceeding x, isJEE Main 2025 · medium

JEE Main 2024

It is known that ∫0^π/2ln (sin x) dx=-(π)/(2)ln 2. Using this, ∫0^πln (1-cos x) dx is equal toJEE Main 2024 · medium
The value of ∫0^4(|x-1|+|x-3|)dx isJEE Main 2024 · medium

JEE Main 2023

The value of 16∫0^1 x [4x] dx, where [ · ] denotes the greatest integer function, isJEE Main 2023 · medium

JEE Main 2022

∫0^π(xsin x)/(1+cos ^2x) dx equalsJEE Main 2022 · hard
∫(x^2-1)/(x^4+x^2+1) dx equals (where C is a constant)JEE Main 2022 · hard
Let f be a continuous function such that f(x)=6x^2+x∫0^1 t f(t) dt+3∫0^1 f(t) dt for all real x. Then f(2) equalsJEE Main 2022 · hard

JEE Main 2021

The value of ∫0^1 xtan ^-1x dx isJEE Main 2021 · medium

JEE Main 2020

Find the value of 3∫0^3|x^2-2x| dx.JEE Main 2020 · medium

JEE Main 2019

Let In=∫0^π/2sin ^n x dx. Then 10 I10 I9 equalsJEE Main 2019 · medium

JEE Main 2018

Let f be twice differentiable on [0,1] with f(0)=1, f(1)=4 and ∫0^1 f(x) dx=13/6. Then ∫0^1 (x^2-x)f''(x) dx equalsJEE Main 2018 · hard

JEE Main 2017

The value of ∫-1^1(x^2/(1+e^x dx isJEE Main 2017 · medium
Evaluate ∫ e^x (1+sin x)/(1+cos x) dx, where C denotes an arbitrary constant.JEE Main 2017 · hard

JEE Main 2016

The value of ∫0^π/2(sin x)/(sin x+cos x) dx isJEE Main 2016 · medium
∫(cos 2x)/((sin x+cos x)^2 dx equals (where C is the constant of integration)JEE Main 2016 · hard

Other Mathematics topics

Area Under Curves 7 Binomial Theorem 12 Complex Numbers 10 Conic Sections 5 Differential Equations 9 Differentiation and Application of Derivatives 19 Limits 9 Matrices and Determinants 19 Permutations and Combinations 10 Probability 9 Quadratic Equations 9 Sequences and Series 9 Sets, Relations and Functions 10 Statistics 6 Straight Lines and Circles 9 Three Dimensional Geometry 14 Trigonometry and Inverse Trigonometric Functions 9 Vector Algebra 8