Integral de $$$- t$$$

Halla $$$\int \left(- t\right)\, dt$$$.

Aplica la regla del factor constante $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$ con $$$c=-1$$$ y $$$f{\left(t \right)} = t$$$:

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

Aplica la regla de la potencia $$$\int t^{n}\, dt = \frac{t^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ con $$$n=1$$$:

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

Por lo tanto,

$$\int{\left(- t\right)d t} = - \frac{t^{2}}{2}$$

Añade la constante de integración:

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

$$$\int \left(- t\right)\, dt = - \frac{t^{2}}{2} + C$$$A