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Maths Definite Integral and Area Under Curves Estimation & Mean Value Theorem Subjective Type

Published by: CGP EDU Academic Team

Published on: August 12, 2026

Prove the following inequalities : –

(i) < <

(ii) 4 ≤ ≤ 2

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

(i) is monotonic decreasing ∴ <

(ii)Let f(x) =

f ′ (x) = > 0 ∀ x ∈ (1, 3)

⇒ f is strictly increasing in (1, 3)  m = least value = f(1) =

M = greatest value = f(3) =  m(b – a) ≤

⇒ 2(2) ≤ ⇒ 4 ≤

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