Definite Integration — JEE Advanced Previous Year Questions

How many JEE Advanced questions come from Definite Integration?

Definite Integration has contributed 24 questions to Joint Entrance Examination (Advanced) papers between 2016 and 2026 — an average of about 2 questions a year. That count is measured from EByAi’s bank of 18,502 JEE Advanced questions, not estimated from a syllabus. Every one of the 24 questions carries a written, step-by-step solution, and each is tagged to Definite Integration within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Definite Integration questions from real JEE Advanced papers

These are 3 real questions from the bank — exactly as asked, with the answer one tap away. All 24 Definite Integration questions (with full written solutions) are available in practice.

1. Question 1 · JEE Advanced 2026

   The value of the definite integral $\underset{0}{\overset{2}{\int }}\frac{1}{3^x+3}dx$ is
   1. (A)$\frac{1}{2}$
   2. (B)$\frac{1}{3}$
   3. (C)$\frac{{\log }_{e}3}{3}$
   4. (D)$\frac{{\log }_{e}3}{2}$
   Show answerAnswer

   Answer: (B) $\frac{1}{3}$

2. Question 2 · JEE Advanced 2023

   Let $f:(0,1)\to \mathbb{R}$ be the function defined as $f(x)=\sqrt{n}$ if $x\in \left[\frac{1}{n+1},\frac{1}{n}\right)$ where $n\in \mathbb{N}$. Let $g:(0,1)\to \mathbb{R}$ be a function such that $\underset{x^2}{\overset{x}{\int }}\sqrt{\frac{1-t}{t}}dt<g(x)<2\sqrt{x}$ for all $x\in (0,1)$. Then $\underset{x\to 0}{\lim }f(x)g(x)$
   1. (A)does NOT exist
   2. (B)is equal to 1
   3. (C)is equal to 2
   4. (D)is equal to 3
   Show answerAnswer

   Answer: (C) is equal to 2

3. Question 3 · JEE Advanced 2016

   The value of $\underset{-\frac{\pi }{2}}{\overset{\frac{\pi }{2}}{\int }}\frac{x^2\cos x}{1+e^x}dx$ is equal to
   1. (A)$$\frac{{\pi }^2}{4}-2$$
   2. (B)$$\frac{{\pi }^2}{4}+2$$
   3. (C)$${\pi }^2-e^{\frac{\pi }{2}}$$
   4. (D)$${\pi }^2+e^{\frac{\pi }{2}}$$
   Show answerAnswer

   Answer: (A) $\frac{{\pi }^2}{4}-2$

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