Integralen av $$$\frac{7 x^{2}}{872}$$$

Bestäm $$$\int \frac{7 x^{2}}{872}\, dx$$$.

Tillämpa konstantfaktorregeln $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ med $$$c=\frac{7}{872}$$$ och $$$f{\left(x \right)} = x^{2}$$$:

$${\color{red}{\int{\frac{7 x^{2}}{872} d x}}} = {\color{red}{\left(\frac{7 \int{x^{2} d x}}{872}\right)}}$$

Tillämpa potensregeln $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ med $$$n=2$$$:

$$\frac{7 {\color{red}{\int{x^{2} d x}}}}{872}=\frac{7 {\color{red}{\frac{x^{1 + 2}}{1 + 2}}}}{872}=\frac{7 {\color{red}{\left(\frac{x^{3}}{3}\right)}}}{872}$$

Alltså,

$$\int{\frac{7 x^{2}}{872} d x} = \frac{7 x^{3}}{2616}$$

Lägg till integrationskonstanten:

$$\int{\frac{7 x^{2}}{872} d x} = \frac{7 x^{3}}{2616}+C$$

$$$\int \frac{7 x^{2}}{872}\, dx = \frac{7 x^{3}}{2616} + C$$$A