JEE Main 2023MathematicsDefinite IntegrationProperties Of Definite IntegrationmediumMCQ

JEE Main 2023Definite Integration Question with Solution

From: JEE Main 2023 (Online) 31st January Evening Shift

Question

Let . If , then is equal to :

Choose an option

Show full solutionCorrect option: B
Correct answer
B2

Step-by-step explanation





\eqalign{ & = {1 \over \alpha }\int\limits_0^\alpha {\left( {x\sqrt {x + \alpha } + x\sqrt x } \right)} dx \cr & = {1 \over \alpha }\int\limits_0^\alpha {\left[ {\left( {x + \alpha - \alpha } \right)\sqrt {x + \alpha } + {x^{{3 \over 2}}}} \right]} dx \cr}



Now,



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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.