Integral of $$$c y^{2}$$$ with respect to $$$y$$$

Find $$$\int c y^{2}\, dy$$$.

Apply the constant multiple rule $$$\int c f{\left(y \right)}\, dy = c \int f{\left(y \right)}\, dy$$$ with $$$c=c$$$ and $$$f{\left(y \right)} = y^{2}$$$:

$${\color{red}{\int{c y^{2} d y}}} = {\color{red}{c \int{y^{2} d y}}}$$

Apply the power rule $$$\int y^{n}\, dy = \frac{y^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=2$$$:

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

Therefore,

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

Add the constant of integration:

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

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