JEE Main 2023MathematicsDefinite IntegrationEasyNumerical

JEE Main 2023 — Definite Integration Question with Solution

JEE Main 2023 (24 Jan Shift 1)

Question

The value of 8π∫0π2cosx2023sinx2023+cosx2023dx is ______.

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Show full solutionCorrect answer: 2
Correct answer
2

Step-by-step explanation

Let

I=8π∫0π2cosx2023sinx2023+cosx2023dx   ...1

Using ∫0af(x)dx=∫0af(a-x)dx

I=8π∫0π2sinx2023sinx2023+cosx2023dx   ...2

Adding 1 and 2, we get

2I=8π∫0π21 dx

⇒2I=8πx0π2

⇒I=2

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About this question

This is a previous-year question from JEE Main 2023, 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.