JEE Main 2020 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 4 September 2020, Shift 1, Maths Q62

Question 62 of 75 in this shift, Maths question 12 of 25.

Let

f(x) = \int \frac{\sqrt{x}}{(1+x)^2}\,\mathrm{d}x

(x \ge 0)

. Then

f(3) - f(1)

is equal to :

(1) $-\frac{\pi}{12} + \frac{1}{2} + \frac{\sqrt{3}}{4}$
(2) $\frac{\pi}{12} + \frac{1}{2} - \frac{\sqrt{3}}{4}$ Official answer
(3) $\frac{\pi}{6} + \frac{1}{2} - \frac{\sqrt{3}}{4}$
(4) $-\frac{\pi}{6} + \frac{1}{2} + \frac{\sqrt{3}}{4}$

Official answer

Option 2

NTA final key (Sep 2020).

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Fractional Powers LCM Substitution

Same idea in other shifts

Asked 5× in all

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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.