Definite Integral/Examples/x squared from 0 to 2
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Example of Definite Integral
- $\ds \int_0^2 x^2 \rd x = \dfrac 8 3$
Proof
| \(\ds \int_0^2 x^2 \rd x\) | \(=\) | \(\ds \intlimits {\dfrac {x^3} 3} 0 2\) | Primitive of Power | |||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {2^3} 3 - \dfrac {0^3} 3\) | Definition of Definite Integral | |||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac 8 3\) | evaluating |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {II}$. Calculus: Exercises $\text {XV}$: $1. \ \text{(a)}$