Exercise · ZW-INTEGRABILITY-OF-CONTINUOUS-FUNCTIONS-003 · ★☆☆ Basic
The integrability theorem for continuous functions requires the domain to be:
Choose one option.
Show answer
- B. A closed, bounded interval \([a,b]\)
Explanation
A closed, bounded interval is required. On \((0,1)\), for instance, \(1/x\) is continuous but unbounded, and on \([1,\infty)\) the Riemann integral is not defined.
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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