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JEE Main 2021 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 4 August 2021, Shift 1, Maths Q86

Question 86 of 90 in this shift, Maths question 26 of 30, Section B.

If

\int\left(\sqrt{\tan x}+\sqrt{\cot x}\right)dx=a\tan^{-1}\left(\frac{\tan x-1}{\sqrt{b\tan x}}\right)+\mathrm{C}

, then the value of

a^4+b^5

is ________. (Here, C is a constant of integration).

Official answer

36

NTA final key.

Chapter: Integrals
Topic: Integration by Substitution
Idea tested: Twin Trigonometric Integrals Substitution

Same idea in other shifts

Asked 2× in all

26 Jul 2022, Shift 2 · Q19The integral $\int\frac{\left(1-\frac{1}{\sqrt{3}}\right)(\cos x-\sin x)}{\left(1+\frac{2}{\sqrt{3}}\sin 2x\right)}dx$ is equal toHardSingle 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.