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JEE Main 2025 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 7 April 2025, Shift 1, Maths Q18

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

The integral

\int_0^{\pi} \frac{(x+3)\sin x}{1+3\cos^2 x}\,dx

is equal to

(1) $\frac{\pi}{\sqrt{3}}(\pi+1)$
(2) $\frac{\pi}{\sqrt{3}}(\pi+2)$
(3) $\frac{\pi}{2\sqrt{3}}(\pi+4)$
(4) $\frac{\pi}{3\sqrt{3}}(\pi+6)$ Official answer

Official answer

Option 4

NTA final key.

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

Same idea in other shifts

Asked 2× in all

31 Jan 2024, Shift 2 · Q26 $\left|\frac{120}{\pi^3}\int_0^{\pi}\frac{x^2\sin x\cos x}{\sin^4x+\cos^4x}dx\right|$ is equal to ____________.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.