Exercise · ZW-DEFINITE-INTEGRAL-007 · ★★☆ Intermediate
What is \(\int_1^3 2x\,dx\)?
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- C. 8
Explanation
An antiderivative of 2x is x²; evaluating from 1 to 3 gives 9 − 1 = 8.
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
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- 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-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?