JEE Main 2021 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 25 February 2021, Shift 1, Maths Q68

Question 68 of 90 in this shift, Maths question 8 of 30, Section A.

The value of

\int_{-1}^{1} x^2 e^{[x^3]}dx

, where [t] denotes the greatest integer

\leq

t, is :

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

Official answer

Option 4

NTA final key.

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

Same idea in other shifts

Asked 29× in all

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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.