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Theorem: Partial Integration

Let $[a,]$ be a closed real interval, let $f,g:[a,b]\to\mathbb R$ be continouosly differentiable functions. Then

$$\int_a^bf(x)g’(x)dx=f(x)g(x)\;\Rule{1px}{4ex}{2ex}^b_a -\int_{a}^{b}g(x)f’(x)dx.$$

Mnemonic Notation

$$\int fdg=fg-\int gdf.$$

| | | | | created: 2020-01-08 11:33:42 | modified: 2020-01-08 11:49:51 | by: bookofproofs | references: [581]

1.Proof: (related to "Partial Integration")

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)

[581] Forster Otto: “Analysis 1, Differential- und Integralrechnung einer Veränderlichen”, Vieweg Studium, 1983