Primitive of Constant Multiple of Function/Proof 2
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Theorem
Let $f$ be a real function which is integrable.
Let $c$ be a constant.
Then:
- $\ds \int c \map f x \rd x = c \int \map f x \rd x$
Proof
From Derivative of Constant Multiple:
- $\map {\dfrac \d {\d x} } {c \map f x} = c \map {\dfrac \d {\d x} } {\map f x}$
The result follows from the definition of primitive.
Sources
- 1945: A. Geary, H.V. Lowry and H.A. Hayden: Advanced Mathematics for Technical Students, Part I ... (previous) ... (next): Chapter $\text {III}$: Integration: Three rules for integration: $\text {I}$
- For a video presentation of the contents of this page, visit the Khan Academy.