integral from 0 to 1 of e^{2x}cos(pix)

Lösung

\int_{0}^{1} e^{2 x} cos (π x) d x

\frac{- 2 e ^{2} - 2}{π ^{2} + 4}

Dezimale

- 1.20970 \dots

Schritte zur Lösung

\int_{0}^{1} e^{2 x} cos (π x) d x

Berechne das unbestimmte Integral:

\int e^{2 x} cos (π x) d x = \frac{π e ^{2 x} sin ( π x )}{π ^{2} + 4} + \frac{2 e ^{2 x} cos ( π x )}{π ^{2} + 4} + C

Berechne die Grenzen:

\int_{0}^{1} e^{2 x} cos (π x) d x = - \frac{2 e ^{2}}{π ^{2} + 4} - \frac{2}{π ^{2} + 4}

= - \frac{2 e ^{2}}{π ^{2} + 4} - \frac{2}{π ^{2} + 4}

Vereinfache

= \frac{- 2 e ^{2} - 2}{π ^{2} + 4}

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