Definite Integral/Examples/Cosine of x from 0 to pi by 2
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Example of Definite Integral
- $\ds \int_0^{\pi / 2} \cos x \rd x = 1$
Proof
| \(\ds \int_0^{\pi / 2} \cos x \rd x\) | \(=\) | \(\ds \bigintlimits {\sin x} 0 {\pi / 2}\) | Primitive of Cosine Function | |||||||||||
| \(\ds \) | \(=\) | \(\ds \sin \dfrac \pi 2 - \sin 0\) | Definition of Definite Integral | |||||||||||
| \(\ds \) | \(=\) | \(\ds 1 - 0\) | Sine of Right Angle, Sine of $0 \degrees$ | |||||||||||
| \(\ds \) | \(=\) | \(\ds 1\) |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {II}$. Calculus: Exercises $\text {XV}$: $1. \ \text{(c)}$