Integral of $$$- 4 y$$$

Find $$$\int \left(- 4 y\right)\, dy$$$.

Apply the constant multiple rule $$$\int c f{\left(y \right)}\, dy = c \int f{\left(y \right)}\, dy$$$ with $$$c=-4$$$ and $$$f{\left(y \right)} = y$$$:

$${\color{red}{\int{\left(- 4 y\right)d y}}} = {\color{red}{\left(- 4 \int{y d y}\right)}}$$

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

$$- 4 {\color{red}{\int{y d y}}}=- 4 {\color{red}{\frac{y^{1 + 1}}{1 + 1}}}=- 4 {\color{red}{\left(\frac{y^{2}}{2}\right)}}$$

Therefore,

$$\int{\left(- 4 y\right)d y} = - 2 y^{2}$$

Add the constant of integration:

$$\int{\left(- 4 y\right)d y} = - 2 y^{2}+C$$

$$$\int \left(- 4 y\right)\, dy = - 2 y^{2} + C$$$A