Integralen av $$$\frac{\cos{\left(\theta \right)}}{1312}$$$

Bestäm $$$\int \frac{\cos{\left(\theta \right)}}{1312}\, d\theta$$$.

Tillämpa konstantfaktorregeln $$$\int c f{\left(\theta \right)}\, d\theta = c \int f{\left(\theta \right)}\, d\theta$$$ med $$$c=\frac{1}{1312}$$$ och $$$f{\left(\theta \right)} = \cos{\left(\theta \right)}$$$:

$${\color{red}{\int{\frac{\cos{\left(\theta \right)}}{1312} d \theta}}} = {\color{red}{\left(\frac{\int{\cos{\left(\theta \right)} d \theta}}{1312}\right)}}$$

Integralen av cosinus är $$$\int{\cos{\left(\theta \right)} d \theta} = \sin{\left(\theta \right)}$$$:

$$\frac{{\color{red}{\int{\cos{\left(\theta \right)} d \theta}}}}{1312} = \frac{{\color{red}{\sin{\left(\theta \right)}}}}{1312}$$

Alltså,

$$\int{\frac{\cos{\left(\theta \right)}}{1312} d \theta} = \frac{\sin{\left(\theta \right)}}{1312}$$

Lägg till integrationskonstanten:

$$\int{\frac{\cos{\left(\theta \right)}}{1312} d \theta} = \frac{\sin{\left(\theta \right)}}{1312}+C$$

$$$\int \frac{\cos{\left(\theta \right)}}{1312}\, d\theta = \frac{\sin{\left(\theta \right)}}{1312} + C$$$A