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Saturday, 31 October

JEE Main · Maths · Integrals

Pure Quadratic Outside and Inside Root Substitution

JEE Main asked Pure Quadratic Outside and Inside Root Substitution once in the 108 shifts Lumi analysed, on 28 Jul 2022, Shift 1. It belongs to Integration by Substitution, in Integrals (Maths).

Updated 2026-10-24

Times asked
1
in 1 shift
Years
1 of 8
First asked
2022
the only year
Pattern
Occasional
asked once so far

Questions on this idea a shift, by year

2017–2026. Asked in 2022. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200’210.04’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20250 of 8
  • 20240 of 18
  • 20230 of 12
  • 20221 of 24
  • 20210 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: calculation.

  • Definite integral with nested radical substitution

Difficulty

Easy 0Medium 0Hard 1

1 of the 1 question had a numerical answer.

Every question

The question

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 28 Jul 2022, Shift 1 · Q24If ∫0315x31+x2+(1+x2)3 dx=α2+β3\int_0^{\sqrt{3}}\frac{15x^3}{\sqrt{1+x^2+\sqrt{(1+x^2)^3}}}\,dx=\alpha\sqrt{2}+\beta\sqrt{3}, where α,β\alpha,\beta are integers,…HardNumerical value

Shift: 28 Jul 2022, Shift 1.

Same topic

Other ideas in Integration by Substitution

Integration by Substitution has 27 ideas JEE Main has asked; 12 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas