Exercise · ZW-DEFINITE-INTEGRAL-002 · ★☆☆ Basic
The definite integral \(\displaystyle\int_a^b f(x)\,dx\) with \(f(x)\ge 0\) represents...
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- D. the area between the graph of f and the x-axis
Explanation
When f is nonnegative, the definite integral is the area of the region bounded by the graph of f, the x-axis and the lines x = a and x = b.
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 \(x=b\).
\[\int_a^b f(x)\,dx=\lim_{n\to\infty}\sum_{i=1}^{n}f(x_i^{*})\,\Delta x\]
More practice problems: definite integral
- ZW-DEFINITE-INTEGRAL-001 What is ∫_-1^1 x dx?
- ZW-DEFINITE-INTEGRAL-003 What is the correct notation for the definite integral of f from a to b?
- ZW-DEFINITE-INTEGRAL-004 What is the definite integral built as a limit of Riemann sums called?
- ZW-DEFINITE-INTEGRAL-005 In Riemann sums, what does Delta x represent?
- ZW-DEFINITE-INTEGRAL-006 What is ∫_0^2 3 dx?
- ZW-DEFINITE-INTEGRAL-007 What is ∫_1^3 2x dx?
- ZW-DEFINITE-INTEGRAL-008 Is it true that if ∫_-1^1 f(x) dx=0 then f(x)=0 for all x∈[-1,1]?
- ZW-DEFINITE-INTEGRAL-009 Which property lets you split the integral of a sum of functions?