Primitive of Constant Multiple of Function/Proof 2

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: $\text {I}$

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