integral from 0 to t of 2t

Lösung

\int_{0}^{t} 2 t d t

t^{2}

Schritte zur Lösung

\int_{0}^{t} 2 t d t

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{t} t d t

Wende die Potenzregel an

= 2 [\frac{t ^{2}}{2}]_{0}^{t}

Berechne die Grenzen:

\frac{t ^{2}}{2}

= 2 \cdot \frac{t ^{2}}{2}

Vereinfache

= t^{2}

\int_{0}^{3} \frac{2 x}{( x ^{2} + 2 ) ^{3}} d x

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