JEE Main 2022 · MathsNumerical answerNumerical valueHardCalculation

JEE Main 28 July 2022, Shift 1, Maths Q24

Question 24 of 90 in this shift, Maths question 24 of 30, Section B.

\int_0^{\sqrt{3}}\frac{15x^3}{\sqrt{1+x^2+\sqrt{(1+x^2)^3}}}\,dx=\alpha\sqrt{2}+\beta\sqrt{3}

, where

\alpha,\beta

are integers, then

\alpha+\beta

is equal to __________.

Official answer

NTA final key (2022 Session 2).

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Pure Quadratic Outside and Inside Root Substitution

Same topic in other shifts

All Integration by Substitution questions

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7 Apr 2025, Shift 2 · Q24If…HardNumerical value
6 Apr 2024, Shift 2 · Q12If $\int\frac{1}{a^2\sin^2x+b^2\cos^2x}dx=\frac{1}{12}\tan^{-1}(3\tan x)+\text{constant}$ , then the maximum value of $a\sin x+b\cos x$ , 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 42 of the 174 JEE Main shifts held from 2017 to 2026.