integral from 0 to 1 of 5^{2t-2}

Lösung

\int_{0}^{1} 5^{2 t - 2} d t

\frac{12}{25 ln ( 5 )}

Dezimale

0.29824 \dots

Schritte zur Lösung

\int_{0}^{1} 5^{2 t - 2} d t

Wende U-Substitution an

= \int_{- 2}^{0} 5^{u} \cdot \frac{1}{2} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{- 2}^{0} 5^{u} d u

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

= \frac{1}{2} [\frac{5 ^{u}}{ln ( 5 )}]_{- 2}^{0}

Berechne die Grenzen:

\frac{24}{25 ln ( 5 )}

= \frac{1}{2} \cdot \frac{24}{25 ln ( 5 )}

Vereinfache

= \frac{12}{25 ln ( 5 )}

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