integral from x to 1 of 3x

Lösung

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

\frac{3 ( 1 - x ^{2} )}{2}

Schritte zur Lösung

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

Entferne die Konstante:

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

= 3 \cdot \int_{x}^{1} x d x

Wende die Potenzregel an

= 3 [\frac{x ^{2}}{2}]_{x}^{1}

Berechne die Grenzen:

\frac{1}{2} - \frac{x ^{2}}{2}

= 3 (\frac{1}{2} - \frac{x ^{2}}{2})

Vereinfache

= \frac{3 ( 1 - x ^{2} )}{2}

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