Integraal van $$$\frac{y^{3}}{8}$$$

Bepaal $$$\int \frac{y^{3}}{8}\, dy$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(y \right)}\, dy = c \int f{\left(y \right)}\, dy$$$ toe met $$$c=\frac{1}{8}$$$ en $$$f{\left(y \right)} = y^{3}$$$:

$${\color{red}{\int{\frac{y^{3}}{8} d y}}} = {\color{red}{\left(\frac{\int{y^{3} d y}}{8}\right)}}$$

Pas de machtsregel $$$\int y^{n}\, dy = \frac{y^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=3$$$:

$$\frac{{\color{red}{\int{y^{3} d y}}}}{8}=\frac{{\color{red}{\frac{y^{1 + 3}}{1 + 3}}}}{8}=\frac{{\color{red}{\left(\frac{y^{4}}{4}\right)}}}{8}$$

Dus,

$$\int{\frac{y^{3}}{8} d y} = \frac{y^{4}}{32}$$

Voeg de integratieconstante toe:

$$\int{\frac{y^{3}}{8} d y} = \frac{y^{4}}{32}+C$$

$$$\int \frac{y^{3}}{8}\, dy = \frac{y^{4}}{32} + C$$$A