JEE Main 2023 — Definite Integration Question with Solution
From: JEE Main 2023 (Online) 10th April Evening Shift
Question
Let be a continuous function satisfying \int_\limits{0}^{t^{2}}\left(f(x)+x^{2}\right) d x=\frac{4}{3} t^{3}, \forall t > 0. Then is equal to :
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
Given that
On differentiating using Leibnitz rule, we get
On substituting for , we get
On differentiating using Leibnitz rule, we get
On substituting for , we get
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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.