Primitive of Cosine of a x + b/Proof 1
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Corollary to Primitive of Cosine Function
- $\ds \int \map \cos {a x + b} \rd x = \frac {\map \sin {a x + b} } a + C$
Proof
\(\ds \int \cos x \rd x\) | \(=\) | \(\ds \sin x + C\) | Primitive of $\cos x$ | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds \int \map \cos {a x + b} \rd x\) | \(=\) | \(\ds \frac 1 a \paren {\map \sin {a x + b} } + C\) | Primitive of Function of $a x + b$ | ||||||||||
\(\ds \) | \(=\) | \(\ds \frac {\map \sin {a x + b} } a + C\) | simplifying |
$\blacksquare$
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: $\text {III}$