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Integraal van $$$\theta \sin{\left(2 \right)}$$$
Gerelateerde rekenmachine: Rekenmachine voor bepaalde en oneigenlijke integralen
Uw invoer
Bepaal $$$\int \theta \sin{\left(2 \right)}\, d\theta$$$.
Oplossing
Pas de constante-veelvoudregel $$$\int c f{\left(\theta \right)}\, d\theta = c \int f{\left(\theta \right)}\, d\theta$$$ toe met $$$c=\sin{\left(2 \right)}$$$ en $$$f{\left(\theta \right)} = \theta$$$:
$${\color{red}{\int{\theta \sin{\left(2 \right)} d \theta}}} = {\color{red}{\sin{\left(2 \right)} \int{\theta d \theta}}}$$
Pas de machtsregel $$$\int \theta^{n}\, d\theta = \frac{\theta^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ toe met $$$n=1$$$:
$$\sin{\left(2 \right)} {\color{red}{\int{\theta d \theta}}}=\sin{\left(2 \right)} {\color{red}{\frac{\theta^{1 + 1}}{1 + 1}}}=\sin{\left(2 \right)} {\color{red}{\left(\frac{\theta^{2}}{2}\right)}}$$
Dus,
$$\int{\theta \sin{\left(2 \right)} d \theta} = \frac{\theta^{2} \sin{\left(2 \right)}}{2}$$
Voeg de integratieconstante toe:
$$\int{\theta \sin{\left(2 \right)} d \theta} = \frac{\theta^{2} \sin{\left(2 \right)}}{2}+C$$
Antwoord
$$$\int \theta \sin{\left(2 \right)}\, d\theta = \frac{\theta^{2} \sin{\left(2 \right)}}{2} + C$$$A