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Integraal van $$$\frac{\sin{\left(x \right)}}{34}$$$
Gerelateerde rekenmachine: Rekenmachine voor bepaalde en oneigenlijke integralen
Uw invoer
Bepaal $$$\int \frac{\sin{\left(x \right)}}{34}\, dx$$$.
Oplossing
Pas de constante-veelvoudregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ toe met $$$c=\frac{1}{34}$$$ en $$$f{\left(x \right)} = \sin{\left(x \right)}$$$:
$${\color{red}{\int{\frac{\sin{\left(x \right)}}{34} d x}}} = {\color{red}{\left(\frac{\int{\sin{\left(x \right)} d x}}{34}\right)}}$$
De integraal van de sinus is $$$\int{\sin{\left(x \right)} d x} = - \cos{\left(x \right)}$$$:
$$\frac{{\color{red}{\int{\sin{\left(x \right)} d x}}}}{34} = \frac{{\color{red}{\left(- \cos{\left(x \right)}\right)}}}{34}$$
Dus,
$$\int{\frac{\sin{\left(x \right)}}{34} d x} = - \frac{\cos{\left(x \right)}}{34}$$
Voeg de integratieconstante toe:
$$\int{\frac{\sin{\left(x \right)}}{34} d x} = - \frac{\cos{\left(x \right)}}{34}+C$$
Antwoord
$$$\int \frac{\sin{\left(x \right)}}{34}\, dx = - \frac{\cos{\left(x \right)}}{34} + C$$$A