integral from 0 to b of e^{-st}

Lösung

\int_{0}^{b} e^{- s t} d t

- \frac{e ^{- b s} - 1}{s}

Schritte zur Lösung

\int_{0}^{b} e^{- s t} d t

Wende U-Substitution an

= \int_{0}^{- s b} - \frac{e ^{u}}{s} d u

Entferne die Konstante:

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

= - \frac{1}{s} \cdot \int_{0}^{- s b} e^{u} d u

Nutze das gemeinsame Integral :

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

= - \frac{1}{s} [e^{u}]_{0}^{- s b}

Vereinfache

- \frac{1}{s} [e^{u}]_{0}^{- s b} : - \frac{[ e ^{u} ] _{0}^{- b s}}{s}

= - \frac{[ e ^{u} ] _{0}^{- b s}}{s}

Berechne die Grenzen:

e^{- b s} - 1

= - \frac{e ^{- b s} - 1}{s}

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

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\int_{1}^{3} arctan (x) d x

\int_{0}^{4} (8 x + x) d x

\int_{- \infty}^{0} 1 d x