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Beliebt Rechnen >

integral from 0 to pi of sin(t)e^{-st}

Lösung

\int_{0}^{π} sin (t) e^{- s t} d t

Lösung

\frac{e ^{- π s} + 1}{s ^{2} + 1}

Schritte zur Lösung

\int_{0}^{π} sin (t) e^{- s t} d t

Berechne das unbestimmte Integral:

\int sin (t) e^{- s t} d t = - \frac{e ^{- s t} cos ( t )}{1 + s ^{2}} - \frac{s e ^{- s t} sin ( t )}{1 + s ^{2}} + C

Berechne die Grenzen:

\int_{0}^{π} sin (t) e^{- s t} d t = \frac{e ^{- π s}}{s ^{2} + 1} - (- \frac{1}{1 + s ^{2}})

= \frac{e ^{- π s}}{s ^{2} + 1} - (- \frac{1}{1 + s ^{2}})

Vereinfache

= \frac{e ^{- π s} + 1}{s ^{2} + 1}

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