Integralen av $$$11 \sin{\left(x \right)}$$$

Bestäm $$$\int 11 \sin{\left(x \right)}\, dx$$$.

Tillämpa konstantfaktorregeln $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ med $$$c=11$$$ och $$$f{\left(x \right)} = \sin{\left(x \right)}$$$:

$${\color{red}{\int{11 \sin{\left(x \right)} d x}}} = {\color{red}{\left(11 \int{\sin{\left(x \right)} d x}\right)}}$$

Integralen av sinus är $$$\int{\sin{\left(x \right)} d x} = - \cos{\left(x \right)}$$$:

$$11 {\color{red}{\int{\sin{\left(x \right)} d x}}} = 11 {\color{red}{\left(- \cos{\left(x \right)}\right)}}$$

Alltså,

$$\int{11 \sin{\left(x \right)} d x} = - 11 \cos{\left(x \right)}$$

Lägg till integrationskonstanten:

$$\int{11 \sin{\left(x \right)} d x} = - 11 \cos{\left(x \right)}+C$$

$$$\int 11 \sin{\left(x \right)}\, dx = - 11 \cos{\left(x \right)} + C$$$A