Integral dari $$$2 \sqrt{x}$$$

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

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

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

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

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

Oleh karena itu,

$$\int{2 \sqrt{x} d x} = \frac{4 x^{\frac{3}{2}}}{3}$$

Tambahkan konstanta integrasi:

$$\int{2 \sqrt{x} d x} = \frac{4 x^{\frac{3}{2}}}{3}+C$$

$$$\int 2 \sqrt{x}\, dx = \frac{4 x^{\frac{3}{2}}}{3} + C$$$A