Primitive of Cosine Function/Proof 2
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Theorem
- $\ds \int \cos x \rd x = \sin x + C$
Proof
\(\ds \int \cos x \rd x\) | \(=\) | \(\ds \frac 1 2 \int \paren {e^{i x} + e^{-i x} } \rd x\) | Euler's Cosine Identity | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac 1 {2 i} \paren {e^{i x} - e^{-i x} } + C\) | Primitive of Exponential of a x | |||||||||||
\(\ds \) | \(=\) | \(\ds \sin x + C\) | Euler's Sine Identity |
$\blacksquare$