JEE Main 2025 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 8 April 2025, Shift 2, Maths Q19

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

The integral

\int_{-1}^{\frac{3}{2}} \left(\left|\pi^2 x \sin(\pi x)\right|\right) dx

is equal to :

(1) $1 + 3\pi$ Official answer
(2) $2 + 3\pi$
(3) $3 + 2\pi$
(4) $4 + \pi$

Official answer

Option 1

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Modulus Function Interval Splitting

Same idea in other shifts

Asked 6× in all

26 Aug 2021, Shift 1 · Q69The value of $\int_{-1/\sqrt{2}}^{1/\sqrt{2}} \left(\left(\frac{x+1}{x-1}\right)^2 + \left(\frac{x-1}{x+1}\right)^2 - 2\right)^{1/2} dx$ …HardSingle correct
25 Feb 2021, Shift 2 · Q86The value of $\int_{-2}^{2} |3x^2 - 3x - 6|\,dx$ is ________.MediumNumerical value
26 Feb 2021, Shift 1 · Q88The value of the integral $\int_0^{\pi}|\sin 2x|\,dx$ is _________.EasyNumerical value
2 Sep 2020, Shift 1 · Q73The integral $\int_{0}^{2}\left||x-1|-x\right|dx$ is equal to ___________.EasyNumerical value
3 Sep 2020, Shift 1 · Q60 $\int_{-\pi}^{\pi}|\pi-|x||dx$ is equal to :EasySingle 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.