Primitive of Square of Cosine Function/Corollary
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Corollary to Primitive of Square of Cosine Function
- $\ds \int \cos^2 x \rd x = \frac {x + \sin x \cos x} 2 + C$
where $C$ is an arbitrary constant.
Proof
\(\ds \int \sin^2 x \rd x\) | \(=\) | \(\ds \frac x 2 + \frac {\sin 2 x} 4 + C\) | Primitive of Square of Cosine Function | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac x 2 + \frac {2 \sin x \cos x} 4 + C\) | Double Angle Formula for Sine | |||||||||||
\(\ds \) | \(=\) | \(\ds \frac {x + \sin x \cos x} 2 + C\) |
$\blacksquare$
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 14$: General Rules of Integration: $14.22$
- 1976: K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists ... (previous) ... (next): $6$. Integral Calculus: Appendix: Table of Fundamental Standard Integrals