Integral de $$$\frac{x^{2}}{16}$$$

Encontre $$$\int \frac{x^{2}}{16}\, dx$$$.

Aplique a regra do múltiplo constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ usando $$$c=\frac{1}{16}$$$ e $$$f{\left(x \right)} = x^{2}$$$:

$${\color{red}{\int{\frac{x^{2}}{16} d x}}} = {\color{red}{\left(\frac{\int{x^{2} d x}}{16}\right)}}$$

Aplique a regra da potência $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=2$$$:

$$\frac{{\color{red}{\int{x^{2} d x}}}}{16}=\frac{{\color{red}{\frac{x^{1 + 2}}{1 + 2}}}}{16}=\frac{{\color{red}{\left(\frac{x^{3}}{3}\right)}}}{16}$$

Portanto,

$$\int{\frac{x^{2}}{16} d x} = \frac{x^{3}}{48}$$

Adicione a constante de integração:

$$\int{\frac{x^{2}}{16} d x} = \frac{x^{3}}{48}+C$$

$$$\int \frac{x^{2}}{16}\, dx = \frac{x^{3}}{48} + C$$$A