integral from 1 to 4 of sqrt(5x)

Lösung

\int_{1}^{4} 5 x d x

\frac{14 5}{3}

Dezimale

10.43498 \dots

Schritte zur Lösung

\int_{1}^{4} 5 x d x

Wende Radikal Regel an:

n ab = n a n b,

angenommen

a \geq 0, b \geq 0

= \int_{1}^{4} 5 x d x

Entferne die Konstante:

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

= 5 \cdot \int_{1}^{4} x d x

Wende die Potenzregel an

= 5 [\frac{2}{3} x^{\frac{3}{2}}]_{1}^{4}

Berechne die Grenzen:

\frac{14}{3}

= 5 \frac{14}{3}

Vereinfache

= \frac{14 5}{3}

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