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Saturday, 31 October

JEE Main · Maths · Integrals

Inverse Trig Simplification Before Parts

JEE Main asked Inverse Trig Simplification Before Parts 2 times in 2 of the 108 shifts Lumi analysed, in 2020 and 2021. It belongs to Integration by Parts, in Integrals (Maths). The longest wait between two years asking it was 1 year.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2020
last in 2021
Pattern
Gone quiet
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020 and 2021. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170.08’200.03’210’220’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 1 in 24 shifts · 2022: 0 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
  • 20220 of 24
  • 20211 of 24
  • 20201 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Integral of simplified inverse trig function
  • Integral of inverse trig function

Difficulty

Easy 0Medium 1Hard 1

Every question was multiple choice.

Every question

All 2 questions

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

  1. 4 Aug 2021, Shift 2 · Q69If ∫sin⁡−1(2x+24x2+8x+13)dx=Atan⁡−1(2x+23)+Blog⁡e(4x2+8x+13)+C\int\sin^{-1}\left(\frac{2x+2}{\sqrt{4x^2+8x+13}}\right)dx=A\tan^{-1}\left(\frac{2x+2}{3}\right)+B\log_e\left(4x^2+8x+13\right)+C (C…MediumSingle correct
  2. 3 Sep 2020, Shift 2 · Q60If ∫sin⁡−1(x1+x)dx=A(x)tan⁡−1(x)+B(x)+C\int \sin^{-1}\left(\sqrt{\frac{x}{1+x}}\right) dx = A(x)\tan^{-1}(\sqrt{x}) + B(x) + C, where C is a constant of integration, then…HardSingle correct

Shifts: 3 Sep 2020, Shift 2, 4 Aug 2021, Shift 2.

Same topic

Other ideas in Integration by Parts

Integration by Parts has 9 ideas JEE Main has asked; 4 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas