Exercise · ZW-DEFINITE-INTEGRAL-004 · ★☆☆ Basic
What is the definite integral built as a limit of Riemann sums called?
Choose one option.
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- B. Riemann integral
Explanation
Bernhard Riemann formalized this construction with sums of rectangles, which is why it is called the Riemann integral.
Review the concept: Definite integral
The definite integral of \(f\) on \([a,b]\) is the limit of the Riemann sums as \(n\to\infty\). It represents the signed net area between the graph of \(f\) and the \(x\)-axis, from \(x=a\) to \(x=b\).
\[\int_a^b f(x)\,dx=\lim_{n\to\infty}\sum_{i=1}^{n}f(x_i^{*})\,\Delta x\]
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