integral from-pi to pi of e^xcos(x)

Lösung

\int_{- π}^{π} e^{x} cos (x) d x

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

Dezimale

- 11.54873 \dots

Schritte zur Lösung

\int_{- π}^{π} e^{x} cos (x) d x

Berechne das unbestimmte Integral:

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

Berechne die Grenzen:

\int_{- π}^{π} e^{x} cos (x) d x = - \frac{e ^{π}}{2} - (- \frac{1}{2 e ^{π}})

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

Vereinfache

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

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