JEE Main 2022 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 26 June 2022, Shift 1, Maths Q24

Question 24 of 90 in this shift, Maths question 24 of 30, Section B.

Let

f(x) = \max\{|x+1|, |x+2|, \ldots, |x+5|\}

. Then

\int_{-6}^{0} f(x)\,dx

is equal to ________.

Official answer

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Integrals of Min and Max Functions

Same topic in other shifts

All Definite Integral Properties questions

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
2 Apr 2026, Shift 1 · Q25If $\alpha=\int_0^{2\sqrt3}\log_2\left(x^2+4\right)dx+\int_2^4\sqrt{2^x-4}\,dx$ , then $\alpha^2$ is equal to __________.HardNumerical value
2 Apr 2026, Shift 2 · Q17The value of $\int_0^{20\pi} (\sin^4 x + \cos^4 x)dx$ is equal to:EasySingle 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
5 Apr 2026, Shift 1 · Q18The value of the integral $\int_0^{\infty} \frac{\log_e(x)}{x^2+4}\,dx$ is:HardSingle correct
6 Apr 2026, Shift 1 · Q18The value of the integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\left(\frac{32\cos^4 x}{1+e^{\sin x}}\right)dx$ is: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 108 of the 174 JEE Main shifts held from 2017 to 2026.