Integraal van $$$3 y^{2}$$$

Bepaal $$$\int 3 y^{2}\, dy$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(y \right)}\, dy = c \int f{\left(y \right)}\, dy$$$ toe met $$$c=3$$$ en $$$f{\left(y \right)} = y^{2}$$$:

$${\color{red}{\int{3 y^{2} d y}}} = {\color{red}{\left(3 \int{y^{2} d y}\right)}}$$

Pas de machtsregel $$$\int y^{n}\, dy = \frac{y^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=2$$$:

$$3 {\color{red}{\int{y^{2} d y}}}=3 {\color{red}{\frac{y^{1 + 2}}{1 + 2}}}=3 {\color{red}{\left(\frac{y^{3}}{3}\right)}}$$

Dus,

$$\int{3 y^{2} d y} = y^{3}$$

Voeg de integratieconstante toe:

$$\int{3 y^{2} d y} = y^{3}+C$$

$$$\int 3 y^{2}\, dy = y^{3} + C$$$A