integral from 0 to pi/2 of e^{-st}sin(t)

Lösung

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

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

Schritte zur Lösung

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

Berechne das unbestimmte Integral:

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

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

Vereinfache

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

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