The difference between the greatest and the least value of …

Maths Definite Integral and Area Under Curves General Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

The difference between the greatest and the least value of the function F(x) = dt on [2, 3] is -

7/2

3/2

Text Solution

Verified by Experts

The correct answer is:

Differentiating the given function, we get

F ′ (x) = [t + 1] t = x – [t + 1] t = 0 = x + 1.

This is positive for all x ∈ [2, 3], so F is an increasing function in this interval. Therefore its greatest value is

F(3) = dt and its least value is F(2) = dt, so that the required difference between these values is

dt – dt = .

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