JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 3 April 2025, Shift 2, Maths Q18

Question 18 of 75 in this shift, Maths question 18 of 25, Section A.

The integral

\int_0^{\pi} \frac{8x\,dx}{4\cos^2 x + \sin^2 x}

is equal to

(1) $\pi^2$
(2) $\frac{3\pi^2}{2}$
(3) $2\pi^2$ Official answer
(4) $4\pi^2$

Official answer

Option 3

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: King's Property

Same idea in other shifts

Asked 3× in all

8 Apr 2025, Shift 2 · Q18Let $f(x)$ be a positive function and $I_1 = \int_{-\frac{1}{2}}^{1} 2x\, f\big(2x(1-2x)\big)\,dx$ and…HardSingle correct
31 Jan 2024, Shift 1 · Q26Let $f:\mathbb{R}\to\mathbb{R}$ be a function defined by $f(x)=\frac{4^x}{4^x+2}$ and…HardNumerical 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 42 of the 174 JEE Main shifts held from 2017 to 2026.