Integraali $$$b d m o \sin{\left(x \right)}$$$:stä muuttujan $$$x$$$ suhteen

Määritä $$$\int b d m o \sin{\left(x \right)}\, dx$$$.

Sovella vakiokertoimen sääntöä $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ käyttäen $$$c=b d m o$$$ ja $$$f{\left(x \right)} = \sin{\left(x \right)}$$$:

$${\color{red}{\int{b d m o \sin{\left(x \right)} d x}}} = {\color{red}{b d m o \int{\sin{\left(x \right)} d x}}}$$

Sinifunktion integraali on $$$\int{\sin{\left(x \right)} d x} = - \cos{\left(x \right)}$$$:

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

Näin ollen,

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

Lisää integrointivakio:

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

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