JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 29 July 2022, Shift 1, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

f(\alpha) = \int_1^{\alpha} \frac{\log_{10} t}{1 + t}\, dt

\alpha > 0

, then

f(e^3) + f(e^{-3})

is equal to :

(1) $9$
(2) $\frac{9}{2}$
(3) $\frac{9}{\log_e(10)}$
(4) $\frac{9}{2\log_e(10)}$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Reciprocal Limits Substitution Trick

Same topic in other shifts

All Definite Integral Properties questions

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5 Apr 2026, Shift 1 · Q18The value of the integral $\int_0^{\infty} \frac{\log_e(x)}{x^2+4}\,dx$ is:HardSingle correct
6 Apr 2026, Shift 1 · Q18The value of the integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\left(\frac{32\cos^4 x}{1+e^{\sin x}}\right)dx$ is:MediumSingle 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.