integral from 0 to t of e^vsin(t-v)

Lösung

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

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

Schritte zur Lösung

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

Berechne das unbestimmte Integral:

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

Berechne die Grenzen:

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

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

Vereinfache

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

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