JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 5 April 2024, Shift 1, Maths Q11

Question 11 of 90 in this shift, Maths question 11 of 30, Section A.

The integral

\int_0^{\pi/4}\frac{136\sin x}{3\sin x+5\cos x}\,dx

is equal to :

(1) $3\pi-10\log_e(2\sqrt2)+10\log_e 5$
(2) $3\pi-30\log_e 2+20\log_e 5$
(3) $3\pi-25\log_e 2+10\log_e 5$
(4) $3\pi-50\log_e 2+20\log_e 5$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Numerator-Denominator Derivative Matching

Same idea in other shifts

Asked 3× in all

9 Apr 2024, Shift 1 · Q8Let $\int\frac{2-\tan x}{3+\tan x}\,dx=\frac{1}{2}\left(\alpha x+\log_e|\beta\sin x+\gamma\cos x|\right)+C$ , where C is the constant of…MediumSingle correct
27 Aug 2021, Shift 2 · Q84If $\int \frac{2e^x + 3e^{-x}}{4e^x + 7e^{-x}}\, dx = \frac{1}{14}\left(ux + v \log_e(4e^x + 7e^{-x})\right) + C$ , where C is a constant…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.