Integraal van $$$\frac{\cos{\left(\theta \right)}}{1312}$$$
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Uw invoer
Bepaal $$$\int \frac{\cos{\left(\theta \right)}}{1312}\, d\theta$$$.
Oplossing
Pas de constante-veelvoudregel $$$\int c f{\left(\theta \right)}\, d\theta = c \int f{\left(\theta \right)}\, d\theta$$$ toe met $$$c=\frac{1}{1312}$$$ en $$$f{\left(\theta \right)} = \cos{\left(\theta \right)}$$$:
$${\color{red}{\int{\frac{\cos{\left(\theta \right)}}{1312} d \theta}}} = {\color{red}{\left(\frac{\int{\cos{\left(\theta \right)} d \theta}}{1312}\right)}}$$
De integraal van de cosinus is $$$\int{\cos{\left(\theta \right)} d \theta} = \sin{\left(\theta \right)}$$$:
$$\frac{{\color{red}{\int{\cos{\left(\theta \right)} d \theta}}}}{1312} = \frac{{\color{red}{\sin{\left(\theta \right)}}}}{1312}$$
Dus,
$$\int{\frac{\cos{\left(\theta \right)}}{1312} d \theta} = \frac{\sin{\left(\theta \right)}}{1312}$$
Voeg de integratieconstante toe:
$$\int{\frac{\cos{\left(\theta \right)}}{1312} d \theta} = \frac{\sin{\left(\theta \right)}}{1312}+C$$
Antwoord
$$$\int \frac{\cos{\left(\theta \right)}}{1312}\, d\theta = \frac{\sin{\left(\theta \right)}}{1312} + C$$$A