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Beliebt Rechnen >

integral from 0 to 20 of 2^{t/(10)}

Lösung

\int_{0}^{20} 2^{\frac{t}{10}} d t

Lösung

\frac{30}{ln ( 2 )}

+1

Dezimale

43.28085 \dots

Schritte zur Lösung

\int_{0}^{20} 2^{\frac{t}{10}} d t

Wende U-Substitution an

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

Entferne die Konstante:

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

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

2^{u + 1} = 2^{1} \cdot 2^{u}

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

Entferne die Konstante:

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

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

Vereinfache

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

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

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

Vereinfache

= 10 [\frac{2 ^{u}}{ln ( 2 )}]_{0}^{2}

Berechne die Grenzen:

\frac{3}{ln ( 2 )}

= 10 \cdot \frac{3}{ln ( 2 )}

Vereinfache

= \frac{30}{ln ( 2 )}

Graph

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