integral from 0 to pi/2 of e^{2x}cos(x)

Lösung

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

\frac{e ^{π} - 2}{5}

Dezimale

4.22813 \dots

Schritte zur Lösung

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

Berechne das unbestimmte Integral:

\int e^{2 x} cos (x) d x = \frac{e ^{2 x} sin ( x )}{5} + \frac{2 e ^{2 x} cos ( x )}{5} + C

Berechne die Grenzen:

\int_{0}^{\frac{π}{2}} e^{2 x} cos (x) d x = \frac{e ^{π}}{5} - \frac{2}{5}

= \frac{e ^{π}}{5} - \frac{2}{5}

Vereinfache

= \frac{e ^{π} - 2}{5}

\int_{1}^{0} (5 x - 1) d x

\int_{0}^{1} (y^{2} - y^{3}) d y

\int_{- 1}^{0} \frac{1}{x + 1} d x

\int_{0}^{1} x^{2} e^{- 10 x} d x

\int_{1}^{2} (3 x - 4) (x - 1) d x