integral from-1 to 0 of 3e^{5t-8}

Lösung

\int_{- 1}^{0} 3 e^{5 t - 8} d t

\frac{3 ( e ^{5} - 1 )}{5 e ^{13}}

Dezimale

0.00019 \dots

Schritte zur Lösung

\int_{- 1}^{0} 3 e^{5 t - 8} d t

Entferne die Konstante:

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

= 3 \cdot \int_{- 1}^{0} e^{5 t - 8} d t

Wende U-Substitution an

= 3 \cdot \int_{- 13}^{- 8} e^{u} \frac{1}{5} d u

Entferne die Konstante:

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

= 3 \cdot \frac{1}{5} \cdot \int_{- 13}^{- 8} e^{u} d u

Nutze das gemeinsame Integral :

\int e^{u} d u = e^{u}

= 3 \cdot \frac{1}{5} [e^{u}]_{- 13}^{- 8}

Vereinfache

3 \cdot \frac{1}{5} [e^{u}]_{- 13}^{- 8} : \frac{3}{5} [e^{u}]_{- 13}^{- 8}

= \frac{3}{5} [e^{u}]_{- 13}^{- 8}

Berechne die Grenzen:

\frac{1}{e ^{8}} - \frac{1}{e ^{13}}

= \frac{3}{5} (\frac{1}{e ^{8}} - \frac{1}{e ^{13}})

Vereinfache

= \frac{3 ( e ^{5} - 1 )}{5 e ^{13}}

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