Q.1 (C)(ii) If f'(x) = 1/x + x and f(1) = 5/2 then f(x) = log x + x²/2 + _____.

Answer: 2 f(x) = ∫(1/x + x)dx = log x + x²/2 + c. Putting x = 1: 5/2 = 0 + 1/2 + c, so c = 2.

Chapter: Integration· Mathematics & Statistics (Commerce) Part 1

If \(f'(x) = \dfrac{1}{x} + x\) and \(f(1) = \dfrac{5}{2}\) then \(f(x) = \log x + \dfrac{x^2}{2} +\) _____.

Q.1 (C)(ii) If \(f'(x) = \dfrac{1}{x} + x\) and \(f(1) = \dfrac{5}{2}\) then \(f(x) = \log x + \dfrac{x^2}{2} +\) _____.

Doubtly Asked 29 Oct 2026 Board exam · March 2024 hsc 12th Save WhatsApp Report

1 answer

Best answer

Answer: 2

\(f(x) = \int\left(\dfrac{1}{x} + x\right)dx = \log x + \dfrac{x^2}{2} + c\). Putting \(x = 1\): \(\dfrac{5}{2} = 0 + \dfrac{1}{2} + c\), so \(c = 2\).

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

Was this answer helpful?

If \(f'(x) = \dfrac{1}{x} + x\) and \(f(1) = \dfrac{5}{2}\) then \(f(x) = \log x + \dfrac{x^2}{2} +\) _____.

1 answer

Your answer