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Theorem: Fundamental Theorem of Calculus
Let $I$ be a real interval and let $F:I\to\mathbb R$ be an antiderivative of a continuous function $f:I\to\mathbb R$. Then, for all $a,b\in I$ the following holds for the Riemann integrals of $f$ on the closed real interval $[a,b]$:
$$\int_a^bf(x)dx=F(b)-F(a).$$
Different Notation
$$\int_a^bf(x)dx=F(x)\;\Rule{1px}{4ex}{2ex}^{b}_{a}.$$
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2
Theorems: 3
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References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
