Exercise · ZW-INTEGRABILITY-OF-CONTINUOUS-FUNCTIONS-002 · ★☆☆ Basic
Compute \(\displaystyle\int_0^1 (3x^2+1)\,dx\).
Choose one option.
Show answer
- A. \(2\)
Explanation
The function is continuous, hence integrable. An antiderivative is \(x^3+x\), giving \(2-0=2\).
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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