integral from 0 to 1 of sqrt(1+15x)

Lösung

\int_{0}^{1} 1 + 15 x d x

\frac{14}{5}

Dezimale

2.8

Schritte zur Lösung

\int_{0}^{1} 1 + 15 x d x

Wende U-Substitution an

= \int_{1}^{16} \frac{u}{15} d u

Entferne die Konstante:

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

= \frac{1}{15} \cdot \int_{1}^{16} u d u

Wende die Potenzregel an

= \frac{1}{15} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{16}

Berechne die Grenzen:

42

= \frac{1}{15} \cdot 42

Vereinfache

= \frac{14}{5}

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