integral from 0 to 5 of 2(11+0.5x)

Lösung

\int_{0}^{5} 2 (11 + 0.5 x) d x

122.5

Schritte zur Lösung

\int_{0}^{5} 2 (11 + 0.5 x) d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{5} 11 + 0.5 x d x

Wende U-Substitution an

= 2 \cdot \int_{11}^{13.5} \frac{u}{0.5} d u

Entferne die Konstante:

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

= 2 \cdot \frac{1}{0.5} \cdot \int_{11}^{13.5} u d u

Vereinfache

= 2 \cdot 2 \cdot \int_{11}^{13.5} u d u

Wende die Potenzregel an

= 2 \cdot 2 [\frac{u ^{2}}{2}]_{11}^{13.5}

Vereinfache

= 4 [0.5 u^{2}]_{11}^{13.5}

Berechne die Grenzen:

30.625

= 4 \cdot 30.625

Vereinfache

= 122.5

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