integral from 3 to x of 9x

Lösung

\int_{3}^{x} 9 x d x

\frac{9 ( x ^{2} - 9 )}{2}

Schritte zur Lösung

\int_{3}^{x} 9 x d x

Entferne die Konstante:

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

= 9 \cdot \int_{3}^{x} x d x

Wende die Potenzregel an

= 9 [\frac{x ^{2}}{2}]_{3}^{x}

Berechne die Grenzen:

\frac{x ^{2}}{2} - \frac{9}{2}

= 9 (\frac{x ^{2}}{2} - \frac{9}{2})

Vereinfache

= \frac{9 ( x ^{2} - 9 )}{2}

\int_{0}^{2} (2 x^{2})^{2} d x

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