JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 24 June 2022, Shift 1, Maths Q27

Question 27 of 90 in this shift, Maths question 27 of 30, Section B.

Let

\max_{0\le x\le 2}\left\{\frac{9-x^2}{5-x}\right\}=\alpha

and

\min_{0\le x\le 2}\left\{\frac{9-x^2}{5-x}\right\}=\beta

. If

\int_{\beta-\frac{8}{3}}^{2\alpha-1}\max\left\{\frac{9-x^2}{5-x}, x\right\}dx=\alpha_1+\alpha_2\log_e\left(\frac{8}{15}\right)

then

\alpha_1+\alpha_2

is equal to ______.

Official answer

NTA final key (2022 Session 1).

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Max/Min Function Integrals

Same topic in other shifts

All Definite Integral Properties questions

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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 42 of the 174 JEE Main shifts held from 2017 to 2026.