$$$- \cos{\left(x \right)}$$$ 的積分

求$$$\int \left(- \cos{\left(x \right)}\right)\, dx$$$。

套用常數倍法則 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$，使用 $$$c=-1$$$ 與 $$$f{\left(x \right)} = \cos{\left(x \right)}$$$：

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

餘弦函數的積分為 $$$\int{\cos{\left(x \right)} d x} = \sin{\left(x \right)}$$$：

$$- {\color{red}{\int{\cos{\left(x \right)} d x}}} = - {\color{red}{\sin{\left(x \right)}}}$$

因此，

$$\int{\left(- \cos{\left(x \right)}\right)d x} = - \sin{\left(x \right)}$$

加上積分常數：

$$\int{\left(- \cos{\left(x \right)}\right)d x} = - \sin{\left(x \right)}+C$$

$$$\int \left(- \cos{\left(x \right)}\right)\, dx = - \sin{\left(x \right)} + C$$$A