Integraal van $$$8 a^{8} w^{8}$$$ met betrekking tot $$$a$$$

Bepaal $$$\int 8 a^{8} w^{8}\, da$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(a \right)}\, da = c \int f{\left(a \right)}\, da$$$ toe met $$$c=8 w^{8}$$$ en $$$f{\left(a \right)} = a^{8}$$$:

$${\color{red}{\int{8 a^{8} w^{8} d a}}} = {\color{red}{\left(8 w^{8} \int{a^{8} d a}\right)}}$$

Pas de machtsregel $$$\int a^{n}\, da = \frac{a^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=8$$$:

$$8 w^{8} {\color{red}{\int{a^{8} d a}}}=8 w^{8} {\color{red}{\frac{a^{1 + 8}}{1 + 8}}}=8 w^{8} {\color{red}{\left(\frac{a^{9}}{9}\right)}}$$

Dus,

$$\int{8 a^{8} w^{8} d a} = \frac{8 a^{9} w^{8}}{9}$$

Voeg de integratieconstante toe:

$$\int{8 a^{8} w^{8} d a} = \frac{8 a^{9} w^{8}}{9}+C$$

$$$\int 8 a^{8} w^{8}\, da = \frac{8 a^{9} w^{8}}{9} + C$$$A