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JEE Advanced Indefinite and Definite Integrals questions with solutions

Techniques of integration and properties of definite integrals. 18 questions from our 2016–2025 JEE Advanced pattern papers, from the Class 12 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Indefinite and Definite Integrals for JEE Main

JEE Advanced 2025

Let f:[0,∞)→mathbb R be continuous and satisfy f(x)=cos x+2∫0^xsin (x-t) f(t) dt. Then f(ln 3)= ______.JEE Advanced 2025 Paper 2 · hard

JEE Advanced 2024

The value of ∫0^1 (ln (1+x))/(1+x^2 dx isJEE Advanced 2024 Paper 2 · medium

JEE Advanced 2023

Match each definite integral in List-I with its value in List-II. List-I (P) ∫0^π/2(sin ^5x)/(sin ^5x+cos ^5x) dx (Q) ∫0^π(xsin x)/(1+cos ^2x) dx (R)…JEE Advanced 2023 Paper 1 · hard

JEE Advanced 2022

Let varphi(t)=∫-t^t(7x^6+10x^4+9x^2/(1+e^x dx for t>0. The value of varphi(1) isJEE Advanced 2022 Paper 2 · medium
For a non-negative integer n let In=∫0^π/2sin ^nx dx.JEE Advanced 2022 Paper 2 · hard

JEE Advanced 2021

Definite integrals has (have) the stated value?JEE Advanced 2021 Paper 1 · hard

JEE Advanced 2020

A function f:mathbb R→mathbb R satisfies f(x)=x^2+2x∫0^1t f(t) dt for all real x. Find ∫0^2f(x) dx.JEE Advanced 2020 Paper 1 · medium

JEE Advanced 2019

Consider the following four definite integrals and their claimed values. Which of the claims is/are correct?JEE Advanced 2019 Paper 1 · hard
For real x define F(x)=∫-1^1|t-x| dt.JEE Advanced 2019 Paper 2 · hard
The value of (16)/(π)∫0^1(ln (1+x))/(1+x^2 dx is ______.JEE Advanced 2019 Paper 2 · medium

JEE Advanced 2018

A continuous function f:[0,1]→mathbb R satisfies f(x)=x+∫0^1 (xt+t^2f(t) dt for all x∈[0,1].JEE Advanced 2018 Paper 1 · hard
Let I=∫0^π/2(xsin xcos x)/(sin ^4x+cos ^4x) dx. Find the value of I.JEE Advanced 2018 Paper 1 · hard
Evaluate ∫0^π(xsin x)/(1+cos ^2x) dx.JEE Advanced 2018 Paper 2 · hard
Match the integrals in List-I with their values in List-II. List-I (P) ∫-π/2^π/2(x^2cos x)/(1+e^x dx (Q) ∫0^π/2(sin x)/(sin x+cos x) dx (R) ∫0^1(ln…JEE Advanced 2018 Paper 2 · hard

JEE Advanced 2017

Let I=∫0^π/2(2sin ^3x+5cos ^3x)/(sin ^3x+cos ^3x) dx. Find the value of (4I)/(π).JEE Advanced 2017 Paper 1 · easy
Let I=∫0^π(xsin x)/(1+cos ^2x) dx. Then the number I is equal toJEE Advanced 2017 Paper 2 · hard
A continuous function f:[0,1]→mathbb R satisfies f(x)=e^x+x∫0^1 t f(t) dt for all x∈[0,1]. Then ∫0^1 f(x) dx equalsJEE Advanced 2017 Paper 2 · hard

JEE Advanced 2016

The value of ∫-π/4^π/4(x+π/4)/(2-cos 2x) dx isJEE Advanced 2016 Paper 1 · medium

Other Mathematics topics

Area Under Curves 13 Binomial Theorem 10 Complex Numbers 24 Conic Sections 34 Differential Equations 18 Differentiation and Application of Derivatives 20 Limits 19 Matrices and Determinants 28 Permutations and Combinations 18 Probability 38 Quadratic Equations 12 Sequences and Series 11 Sets, Relations and Functions 8 Straight Lines and Circles 10 Three Dimensional Geometry 22 Trigonometry and Inverse Trigonometric Functions 18 Vector Algebra 9