integral from 0 to t of-8e^ssin(t-s)

Lösung

\int_{0}^{t} - 8 e^{s} sin (t - s) d s

- 4 e^{t} + 8 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

Schritte zur Lösung

\int_{0}^{t} - 8 e^{s} sin (t - s) d s

Berechne das unbestimmte Integral:

\int - 8 e^{s} sin (t - s) d s = - 8 (\frac{e ^{s} cos ( - s + t )}{2} + \frac{e ^{s} sin ( - s + t )}{2}) + C

Berechne die Grenzen:

\int_{0}^{t} - 8 e^{s} sin (t - s) d s = - 4 e^{t} - (- 8 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t)))

= - 4 e^{t} - (- 8 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t)))

Vereinfache

= - 4 e^{t} + 8 (\frac{1}{2} cos (t) + \frac{1}{2} sin (t))

\int \frac{x - 3}{x ^{2} - 6 x - 1} d x

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