Q.1 (C) (iii) If f'(x)=x²+5 and f(0)=-1 then f(x)= _____.

Answer: x³/3+5x-1 f(x)=∫(x²+5)dx=x³/3+5x+c . f(0)=-1⇒ c=-1 . So f(x)=x³/3+5x-1 .

If \(f'(x)=x^2+5\) and \(f(0)=-1\) then \(f(x)=\) _____.

Q.1 (C) (iii) If \(f'(x)=x^2+5\) and \(f(0)=-1\) then \(f(x)=\) _____.

Doubtly Asked 28 Oct 2026 Board exam · March 2025 hsc 12th Save WhatsApp Report

Best answer

Answer: \(\frac{x^3}{3}+5x-1\)

\(f(x)=\int(x^2+5)dx=\frac{x^3}{3}+5x+c\). \(f(0)=-1\Rightarrow c=-1\). So \(f(x)=\frac{x^3}{3}+5x-1\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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