Integraal van $$$x_{0}^{4} y_{0}^{4}$$$ met betrekking tot $$$x_{0}$$$

Bepaal $$$\int x_{0}^{4} y_{0}^{4}\, dx_{0}$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(x_{0} \right)}\, dx_{0} = c \int f{\left(x_{0} \right)}\, dx_{0}$$$ toe met $$$c=y_{0}^{4}$$$ en $$$f{\left(x_{0} \right)} = x_{0}^{4}$$$:

$${\color{red}{\int{x_{0}^{4} y_{0}^{4} d x_{0}}}} = {\color{red}{y_{0}^{4} \int{x_{0}^{4} d x_{0}}}}$$

Pas de machtsregel $$$\int x_{0}^{n}\, dx_{0} = \frac{x_{0}^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=4$$$:

$$y_{0}^{4} {\color{red}{\int{x_{0}^{4} d x_{0}}}}=y_{0}^{4} {\color{red}{\frac{x_{0}^{1 + 4}}{1 + 4}}}=y_{0}^{4} {\color{red}{\left(\frac{x_{0}^{5}}{5}\right)}}$$

Dus,

$$\int{x_{0}^{4} y_{0}^{4} d x_{0}} = \frac{x_{0}^{5} y_{0}^{4}}{5}$$

Voeg de integratieconstante toe:

$$\int{x_{0}^{4} y_{0}^{4} d x_{0}} = \frac{x_{0}^{5} y_{0}^{4}}{5}+C$$

$$$\int x_{0}^{4} y_{0}^{4}\, dx_{0} = \frac{x_{0}^{5} y_{0}^{4}}{5} + C$$$A