Definite Integration — JEE Main Previous Year Questions

How many JEE Main questions come from Definite Integration?

Definite Integration has contributed 278 questions to Joint Entrance Examination (Main) papers between 2016 and 2026 — an average of about 25 questions a year. That count is measured from EByAi’s bank of 55,289 JEE Main questions, not estimated from a syllabus. Every one of the 278 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 Main papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 278 Definite Integration questions (with full written solutions) are available in practice.

1. Question 1 · JEE Main 2026

   The value of $\underset{0}{\overset{20\pi }{\int }}({\sin }^{4}x+{\cos }^{4}x)dx$ is equal to:
   1. (A)$\frac{15\pi }{2}$
   2. (B)$25\pi$
   3. (C)$15\pi$
   4. (D)$\frac{25\pi }{2}$
   Show answerAnswer

   Answer: (C) $15\pi$

2. Question 2 · JEE Main 2026

   The integral $\underset{0}{\overset{1}{\int }}{\cot }^{-1}\left(1+x+x^2\right)dx$ is equal to :
   1. (A)$$2{\tan }^{-1}2+\frac{1}{2}{\log }_e\left(\frac{5}{4}\right)+\frac{\pi }{2}$$
   2. (B)$$2{\tan }^{-1}2+\frac{1}{2}{\log }_e\left(\frac{5}{4}\right)-\frac{\pi }{2}$$
   3. (C)$$2{\tan }^{-1}2-\frac{1}{2}{\log }_e\left(\frac{5}{4}\right)+\frac{\pi }{2}$$
   4. (D)$$2{\tan }^{-1}2-\frac{1}{2}{\log }_e\left(\frac{5}{4}\right)-\frac{\pi }{2}$$
   Show answerAnswer

   Answer: (D) $2{\tan }^{-1}2-\frac{1}{2}{\log }_e\left(\frac{5}{4}\right)-\frac{\pi }{2}$

3. Question 3 · JEE Main 2026

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

   Answer: (B) $\frac{\pi {\log }_e(2)}{4}$

4. Question 4 · JEE Main 2026

   The value of the integral $\underset{-1}{\overset{1}{\int }}\left(\frac{x^3+|x|+1}{x^2+2|x|+1}\right)\mathrm{d}x$ is equal to:
   1. (A)$3{\log }_{\mathrm{e}}2$
   2. (B)$2{\log }_{\mathrm{e}}2$
   3. (C)$5{\log }_{\mathrm{e}}3$
   4. (D)$3{\log }_{\mathrm{e}}3$
   Show answerAnswer

   Answer: (B) $2{\log }_{\mathrm{e}}2$

5. Question 5 · JEE Main 2026

   The value of the integral ${\int }_{\frac{\pi }{24}}^{\frac{5\pi }{24}}\frac{\mathrm{d}x}{1+\sqrt[3]{\tan 2x}}$ is :
   1. (A)$\frac{\pi }{3}$
   2. (B)$\frac{\pi }{18}$
   3. (C)$\frac{\pi }{6}$
   4. (D)$\frac{\pi }{12}$
   Show answerAnswer

   Answer: (D) $\frac{\pi }{12}$

Definite Integration questions by year

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