Definite Integral/Examples/Reciprocal of x from 1 to e
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Example of Definite Integral
- $\ds \int_1^e \dfrac {\d x} x = 1$
Proof
| \(\ds \int_1^e \dfrac {\d x} x\) | \(=\) | \(\ds \bigintlimits {\ln x} 1 e\) | Primitive of Reciprocal | |||||||||||
| \(\ds \) | \(=\) | \(\ds \ln e - \ln 1\) | Definition of Definite Integral | |||||||||||
| \(\ds \) | \(=\) | \(\ds 1 - 0\) | Definition of Natural Logarithm, Natural Logarithm of 1 is 0 | |||||||||||
| \(\ds \) | \(=\) | \(\ds 1\) |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {II}$. Calculus: Exercises $\text {XV}$: $1. \ \text{(d)}$