JEE Main 2024MathematicsDefinite IntegrationHardMCQ

JEE Main 2024 — Definite Integration Question with Solution

JEE Main 2024 (30 Jan Shift 1)

Question

The value of limn→∞∑k=1nn3n2+k2n2+3k2 is :

Choose an option

Show full solutionCorrect option: B
Correct answer
B13π8(43+3)

Step-by-step explanation

Given, limn→∞∑k=1nn3n2+k2n2+3k2

=limn→∞1n∑k=1n11+k2n21+3·k2n2

Now, using limit as a sum integral we get,

=∫01dx1+x21+3x2

=12∫0131+3x2-11+x2dx

=12∫011132+x2-11+x2dx

=123tan-13x-tan-1x01

=123tan-13-tan-11

=123·π3-π4

=12π3-π4

=13π8·(43+3)

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About this question

This is a previous-year question from JEE Main 2024, 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.