JEE Main 2022 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 25 July 2022, Shift 2, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

Let

[t]

denote the greatest integer less than or equal to

t

. Then the value of the integral

\int_{-3}^{101}\left([\sin(\pi x)]+e^{[\cos(2\pi x)]}\right)dx

is equal to

(1) $\frac{52(1-e)}{e}$
(2) $\frac{52}{e}$ Official answer
(3) $\frac{52(2+e)}{e}$
(4) $\frac{104}{e}$

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 29× in all

2 Apr 2026, Shift 1 · Q19Let $[\cdot]$ denote the greatest integer function. Then the value of $\int_0^3\left(\frac{e^x+e^{-x}}{[x]!}\right)dx$ is :MediumSingle correct
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
30 Jan 2024, Shift 1 · Q25The value of $9\int_0^9\left[\sqrt{\frac{10x}{x+1}}\right]dx$ , where $[t]$ denotes the greatest integer less than or equal to $t$ , is…HardNumerical value
8 Apr 2023, Shift 1 · Q24Let $[t]$ denote the greatest integer $\le t$ . Then $\frac{2}{\pi}\int_{\pi/6}^{5\pi/6}(8[\operatorname{cosec}x]-5[\cot x])\,dx$ is equal…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

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 108 of the 174 JEE Main shifts held from 2017 to 2026.