integral from 0 to 1 of 4^{3x}

Lösung

\int_{0}^{1} 4^{3 x} d x

\frac{21}{2 ln ( 2 )}

Dezimale

15.14829 \dots

Schritte zur Lösung

\int_{0}^{1} 4^{3 x} d x

Vereinfache

4^{3 x} : 6 4^{x}

= \int_{0}^{1} 6 4^{x} d x

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

= [\frac{6 4 ^{x}}{ln ( 64 )}]_{0}^{1}

\frac{6 4 ^{x}}{ln ( 64 )} = \frac{2 ^{6 x - 1}}{3 ln ( 2 )}

= [\frac{2 ^{6 x - 1}}{3 ln ( 2 )}]_{0}^{1}

Berechne die Grenzen:

\frac{21}{2 ln ( 2 )}

= \frac{21}{2 ln ( 2 )}

\int_{- 1}^{x} 1 - ∣ x ∣ d x

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