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