integral from 0 to b of (7x)/8

Lösung

\int_{0}^{b} \frac{7 x}{8} d x

\frac{7 b ^{2}}{16}

Schritte zur Lösung

\int_{0}^{b} \frac{7 x}{8} d x

Entferne die Konstante:

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

= \frac{7}{8} \cdot \int_{0}^{b} x d x

Wende die Potenzregel an

= \frac{7}{8} [\frac{x ^{2}}{2}]_{0}^{b}

Berechne die Grenzen:

\frac{b ^{2}}{2}

= \frac{7}{8} \cdot \frac{b ^{2}}{2}

Vereinfache

= \frac{7 b ^{2}}{16}

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