JEE Main 2026 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 2 April 2026, Shift 1, Maths Q19

Question 19 of 75 in this shift, Maths question 19 of 25, Section A.

Let

[\cdot]

denote the greatest integer function. Then the value of

\int_0^3\left(\frac{e^x+e^{-x}}{[x]!}\right)dx

is :

(1) $e^2+e^3-\frac{1}{e^2}-\frac{1}{e^3}$
(2) $\frac12\left(e^2+e^3-\frac{1}{e^2}-\frac{1}{e^3}\right)$ Official answer
(3) $e^2+e^3-\frac{1}{2e^2}-\frac{1}{2e^3}$
(4) $\frac12\left(e^2+e^3\right)-\frac{1}{e^2}-\frac{1}{e^3}$

Official answer

Option 2

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Greatest Integer Function Integrals

Same idea in other shifts

Asked 9× in all

4 Apr 2026, Shift 1 · Q19Let $\int_{-2}^{2}\left(|\sin x|+[x\sin x]\right)dx=2(3-\cos 2)+\beta$ , where $[\cdot]$ is the greatest integer function. Then…HardSingle correct
2 Apr 2025, Shift 1 · Q23Let $[\cdot]$ denote the greatest integer function. If $\int_0^{e^3}\left[\frac{1}{e^{x-1}}\right]dx=\alpha-\log_e2$ , then $\alpha^3$ is…MediumNumerical value
3 Apr 2025, Shift 1 · Q19Let the domain of the function $f(x) = \log_2 \log_4 \log_6 (3 + 4x - x^2)$ be $(a, b)$ . If…HardSingle correct
6 Apr 2024, Shift 2 · Q25Let $[t]$ denote the largest integer less than or equal to $t$ . If…HardNumerical value
8 Apr 2023, Shift 2 · Q26Let $[t]$ denote the greatest integer function. If $\int_0^{2.4}[x^2]\,dx = \alpha + \beta\sqrt{2} + \gamma\sqrt{3} + \delta\sqrt{5}$ ,…MediumNumerical value
29 Jun 2022, Shift 1 · Q17 $\int_0^5 \cos\left(\pi\left(x - \left[\frac{x}{2}\right]\right)\right)dx$ , where $[t]$ denotes greatest integer less than or equal to…MediumSingle correct
3 Aug 2021, Shift 2 · Q84If $[x]$ denotes the greatest integer $\le x$ , then the value of $\int_{-2}^{4}\left|[x] - x\right|dx$ is $\underline{\hspace{2em}}$ .MediumNumerical value
16 Mar 2021, Shift 2 · Q74Consider the integral $I=\int_0^{10}\frac{[x]\,e^{[x]}}{e^{x-1}}\,dx$ , where $[x]$ denotes the greatest integer less than or equal to $x$ .…MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.