Exercise · ZW-INTEGRABILITY-OF-CONTINUOUS-FUNCTIONS-004 · ★☆☆ Basic
Compute \(\displaystyle\int_1^3 \frac1x\,dx\), which exists because \(1/x\) is continuous on \([1,3]\).
Choose one option.
Show answer
- D. \(\ln 3\)
Explanation
An antiderivative of \(1/x\) is \(\ln x\), so the integral equals \(\ln 3-\ln 1=\ln 3\).
Review the concept: Integrability of continuous functions
Result stating that every function \(f\) continuous on a closed, bounded interval \([a,b]\) is Riemann integrable there.
\[f\text{ continuous on }[a,b]\ \Rightarrow\ \int_a^b f(x)\,dx\text{ exists}\]
More practice problems: integrability of continuous functions
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