integral from-1 to 1 of |5^x-2^x|

Lösung

\int_{- 1}^{1} ∣ 5^{x} - 2^{x} ∣ d x

\frac{32 ln ( 2 ) - 5 ln ( 5 )}{10 ln ( 5 ) ln ( 2 )}

Dezimale

1.26692 \dots

Schritte zur Lösung

\int_{- 1}^{1} ∣ 5^{x} - 2^{x} ∣ d x

Entferne die Extremwerte

= \int_{- 1}^{0} - 5^{x} + 2^{x} d x + \int_{0}^{1} 5^{x} - 2^{x} d x

\int_{- 1}^{0} - 5^{x} + 2^{x} d x = - \frac{4}{5 ln ( 5 )} + \frac{1}{2 ln ( 2 )}

\int_{0}^{1} 5^{x} - 2^{x} d x = \frac{4}{ln ( 5 )} - \frac{1}{ln ( 2 )}

= - \frac{4}{5 ln ( 5 )} + \frac{1}{2 ln ( 2 )} + \frac{4}{ln ( 5 )} - \frac{1}{ln ( 2 )}

Vereinfache

- \frac{4}{5 ln ( 5 )} + \frac{1}{2 ln ( 2 )} + \frac{4}{ln ( 5 )} - \frac{1}{ln ( 2 )} : \frac{32 ln ( 2 ) - 5 ln ( 5 )}{10 ln ( 5 ) ln ( 2 )}

= \frac{32 ln ( 2 ) - 5 ln ( 5 )}{10 ln ( 5 ) ln ( 2 )}

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