integral from 0 to x of t/2

Lösung

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

\frac{x ^{2}}{4}

Schritte zur Lösung

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

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{0}^{x} t d t

Wende die Potenzregel an

= \frac{1}{2} [\frac{t ^{2}}{2}]_{0}^{x}

Berechne die Grenzen:

\frac{x ^{2}}{2}

= \frac{1}{2} \cdot \frac{x ^{2}}{2}

Vereinfache

= \frac{x ^{2}}{4}

\int_{0}^{2} (t i + e^{t} j - t e^{t} k) d t

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