JEE Main 2020MathematicsDefinite IntegrationProperties Of Definite IntegrationmediumMCQ

JEE Main 2020 — Definite Integration Question with Solution

From: JEE Main 2020 (Online) 7th January Morning Slot

Question

If ƒ(a + b + 1 - x) = ƒ(x), for all x, where a and b are fixed positive real numbers, then

is equal to:

Choose an option

Show full solutionCorrect option: A
Correct answer
A

Step-by-step explanation

I = ...(1)

x a + b - x

I =

I = .....(2)

[As ƒ(x) = ƒ(a + b + 1 - x)

ƒ(x + 1) = ƒ(a + b - x)]

Adding (1) and (2) we get

2I =

I =

I =

I =

I =

Let x = t + 1

I =

=

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About this question

This is a previous-year question from JEE Main 2020, covering the Definite Integration chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.