Integraal van $$$- \frac{53 x}{2}$$$

Bepaal $$$\int \left(- \frac{53 x}{2}\right)\, dx$$$.

Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=- \frac{53}{2}$$$ en $$$f{\left(x \right)} = x$$$:

$${\color{red}{\int{\left(- \frac{53 x}{2}\right)d x}}} = {\color{red}{\left(- \frac{53 \int{x d x}}{2}\right)}}$$

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

$$- \frac{53 {\color{red}{\int{x d x}}}}{2}=- \frac{53 {\color{red}{\frac{x^{1 + 1}}{1 + 1}}}}{2}=- \frac{53 {\color{red}{\left(\frac{x^{2}}{2}\right)}}}{2}$$

Dus,

$$\int{\left(- \frac{53 x}{2}\right)d x} = - \frac{53 x^{2}}{4}$$

Voeg de integratieconstante toe:

$$\int{\left(- \frac{53 x}{2}\right)d x} = - \frac{53 x^{2}}{4}+C$$

$$$\int \left(- \frac{53 x}{2}\right)\, dx = - \frac{53 x^{2}}{4} + C$$$A