integral from 0 to 8 of 11000e^{-0.019t}

Lösung

\int_{0}^{8} 11000 e^{- 0.019 t} d t

81638.36378 \dots

Schritte zur Lösung

\int_{0}^{8} 11000 e^{- 0.019 t} d t

Entferne die Konstante:

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

= 11000 \cdot \int_{0}^{8} e^{- 0.019 t} d t

Wende U-Substitution an

= 11000 \cdot \int_{0}^{- 0.152} - \frac{1}{0.019} e^{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= 11000 (- \int_{- 0.152}^{0} - \frac{1}{0.019} e^{u} d u)

Entferne die Konstante:

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

= 11000 (- (- \frac{1}{0.019} \cdot \int_{- 0.152}^{0} e^{u} d u))

Vereinfache

= 11000 (- (- 52.63157 \dots \cdot \int_{- 0.152}^{0} e^{u} d u))

Nutze das gemeinsame Integral :

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

= 11000 (- (- 52.63157 \dots [e^{u}]_{- 0.152}^{0}))

Vereinfache

= 578947.36842 \dots [e^{u}]_{- 0.152}^{0}

Berechne die Grenzen:

0.14101 \dots

= 578947.36842 \dots \cdot 0.14101 \dots

Vereinfache

= 81638.36378 \dots

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