Integral von $$$- \cos{\left(x \right)}$$$

Bestimme $$$\int \left(- \cos{\left(x \right)}\right)\, dx$$$.

Wende die Konstantenfaktorregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ mit $$$c=-1$$$ und $$$f{\left(x \right)} = \cos{\left(x \right)}$$$ an:

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

Das Integral des Kosinus ist $$$\int{\cos{\left(x \right)} d x} = \sin{\left(x \right)}$$$:

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

Daher,

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

Fügen Sie die Integrationskonstante hinzu:

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

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