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

Lösung

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

\frac{e ^{\frac{π}{2}} + 1}{2}

Dezimale

2.90523 \dots

Schritte zur Lösung

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

Berechne das unbestimmte Integral:

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

Berechne die Grenzen:

\int_{0}^{\frac{π}{2}} e^{x} sin (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}

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