Integral dari $$$2 - \frac{x}{2}$$$

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

Integralkan suku demi suku:

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

Terapkan aturan konstanta $$$\int c\, dx = c x$$$ dengan $$$c=2$$$:

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

Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=\frac{1}{2}$$$ dan $$$f{\left(x \right)} = x$$$:

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

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

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

Oleh karena itu,

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

Sederhanakan:

$$\int{\left(2 - \frac{x}{2}\right)d x} = \frac{x \left(8 - x\right)}{4}$$

Tambahkan konstanta integrasi:

$$\int{\left(2 - \frac{x}{2}\right)d x} = \frac{x \left(8 - x\right)}{4}+C$$

$$$\int \left(2 - \frac{x}{2}\right)\, dx = \frac{x \left(8 - x\right)}{4} + C$$$A