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

Lösung

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

\frac{26}{ln ( 3 )}

Dezimale

23.66621 \dots

Schritte zur Lösung

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

Vereinfache

3^{x - 1} : 3^{x} \cdot 3^{- 1}

= \int_{1}^{4} 3^{x} \cdot 3^{- 1} d x

Entferne die Konstante:

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

= 3^{- 1} \cdot \int_{1}^{4} 3^{x} d x

Wende Exponentenregel an:

a^{- 1} = \frac{1}{a}

= \frac{1}{3} \cdot \int_{1}^{4} 3^{x} d x

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

= \frac{1}{3} [\frac{3 ^{x}}{ln ( 3 )}]_{1}^{4}

Berechne die Grenzen:

\frac{78}{ln ( 3 )}

= \frac{1}{3} \cdot \frac{78}{ln ( 3 )}

Vereinfache

= \frac{26}{ln ( 3 )}

\int_{1}^{3} \frac{5}{x} d x

\int_{- 3}^{2} x^{2} + x - 6 d x

\int_{0}^{2} \frac{4 x + 8}{x ^{2} + 4} d x

\int_{0}^{\frac{1}{2}} e^{- x^{2}} d x

\int_{0}^{x} x f (t) d t