integral from 0 to 30 of 1.03^x

Lösung

\int_{0}^{30} 1.0 3^{x} d x

48.28553 \dots

Schritte zur Lösung

\int_{0}^{30} 1.0 3^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= [\frac{1.0 3 ^{x}}{ln ( 1.03 )}]_{0}^{30}

\frac{1.0 3 ^{x}}{ln ( 1.03 )} = 33.83087 \dots \cdot 1.0 3^{x}

= [33.83087 \dots \cdot 1.0 3^{x}]_{0}^{30}

Berechne die Grenzen:

48.28553 \dots

= 48.28553 \dots