Integral dari $$$2 x^{2}$$$

Temukan $$$\int 2 x^{2}\, dx$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=2$$$ dan $$$f{\left(x \right)} = x^{2}$$$:

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

Terapkan aturan pangkat $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ dengan $$$n=2$$$:

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

Oleh karena itu,

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

Tambahkan konstanta integrasi:

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

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