integral from a to b of g(x)

Lösung

\int_{a}^{b} g (x) d x

\frac{g ( b ^{2} - a ^{2} )}{2}

Schritte zur Lösung

\int_{a}^{b} gx d x

Entferne die Konstante:

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

= g \cdot \int_{a}^{b} x d x

Wende die Potenzregel an

= g [\frac{x ^{2}}{2}]_{a}^{b}

Berechne die Grenzen:

\frac{b ^{2}}{2} - \frac{a ^{2}}{2}

= g (\frac{b ^{2}}{2} - \frac{a ^{2}}{2})

Vereinfache

= \frac{g ( b ^{2} - a ^{2} )}{2}

\int_{125}^{1} x^{3} d x

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