Integraal van $$$\frac{\sqrt{2}}{2}$$$ met betrekking tot $$$t$$$

De rekenmachine zal de integraal/primitieve van $$$\frac{\sqrt{2}}{2}$$$ met betrekking tot $$$t$$$ bepalen, waarbij de stappen worden getoond.

Bepaal $$$\int \frac{\sqrt{2}}{2}\, dt$$$.

Pas de constantenregel $$$\int c\, dt = c t$$$ toe met $$$c=\frac{\sqrt{2}}{2}$$$:

$${\color{red}{\int{\frac{\sqrt{2}}{2} d t}}} = {\color{red}{\left(\frac{\sqrt{2} t}{2}\right)}}$$

Dus,

$$\int{\frac{\sqrt{2}}{2} d t} = \frac{\sqrt{2} t}{2}$$

Voeg de integratieconstante toe:

$$\int{\frac{\sqrt{2}}{2} d t} = \frac{\sqrt{2} t}{2}+C$$

$$$\int \frac{\sqrt{2}}{2}\, dt = \frac{\sqrt{2} t}{2} + C$$$A

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