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Beliebt Rechnen >

integral from 0 to pi/2 of e^xcos(x)

Lösung

\int_{0}^{\frac{π}{2}} e^{x} cos (x) d x

Lösung

\frac{e ^{\frac{π}{2}} - 1}{2}

+1

Dezimale

1.90523 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{2}} 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_{0}^{\frac{π}{2}} e^{x} cos (x) d x = \frac{e ^{\frac{π}{2}}}{2} - \frac{1}{2}

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

Vereinfache

= \frac{e ^{\frac{π}{2}} - 1}{2}

Graph

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