Integral dari $$$- 2 f x + 4$$$ terhadap $$$x$$$

Temukan $$$\int \left(- 2 f x + 4\right)\, dx$$$.

Integralkan suku demi suku:

$${\color{red}{\int{\left(- 2 f x + 4\right)d x}}} = {\color{red}{\left(\int{4 d x} - \int{2 f x d x}\right)}}$$

Terapkan aturan konstanta $$$\int c\, dx = c x$$$ dengan $$$c=4$$$:

$$- \int{2 f x d x} + {\color{red}{\int{4 d x}}} = - \int{2 f x d x} + {\color{red}{\left(4 x\right)}}$$

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

$$4 x - {\color{red}{\int{2 f x d x}}} = 4 x - {\color{red}{\left(2 f \int{x d x}\right)}}$$

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

$$- 2 f {\color{red}{\int{x d x}}} + 4 x=- 2 f {\color{red}{\frac{x^{1 + 1}}{1 + 1}}} + 4 x=- 2 f {\color{red}{\left(\frac{x^{2}}{2}\right)}} + 4 x$$

Oleh karena itu,

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

Sederhanakan:

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

Tambahkan konstanta integrasi:

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

$$$\int \left(- 2 f x + 4\right)\, dx = x \left(- f x + 4\right) + C$$$A