integral from 0 to pi/4 of e^xsin(e^x)

Lösung

\int_{0}^{\frac{π}{4}} e^{x} sin (e^{x}) d x

- cos (e^{\frac{π}{4}}) + cos (1)

Dezimale

1.12335 \dots

Schritte zur Lösung

\int_{0}^{\frac{π}{4}} e^{x} sin (e^{x}) d x

Wende U-Substitution an

= \int_{1}^{e^{\frac{π}{4}}} sin (u) d u

Nutze das gemeinsame Integral :

\int sin (u) d u = - cos (u)

= [- cos (u)]_{1}^{e^{\frac{π}{4}}}

Berechne die Grenzen:

- cos (e^{\frac{π}{4}}) + cos (1)

= - cos (e^{\frac{π}{4}}) + cos (1)

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