integral from-3 to 3 of e^{u+3}

Lösung

\int_{- 3}^{3} e^{u + 3} d u

e^{6} - 1

Dezimale

402.42879 \dots

Schritte zur Lösung

\int_{- 3}^{3} e^{u + 3} d u

e^{u + 3} = e^{3} e^{u}

= \int_{- 3}^{3} e^{3} e^{u} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= e^{3} \cdot \int_{- 3}^{3} e^{u} d u

Nutze das gemeinsame Integral :

\int e^{u} d u = e^{u}

= e^{3} [e^{u}]_{- 3}^{3}

Berechne die Grenzen:

e^{3} - \frac{1}{e ^{3}}

= e^{3} (e^{3} - \frac{1}{e ^{3}})

Vereinfache

= e^{6} - 1

\int_{0}^{2} e^{x} x d x

\int_{0}^{2} 4 + x^{2}^{3} d x

\int_{0}^{5} 6 e^{3 x} d x

\int_{1}^{3} 8 x^{2} d x

\int_{0}^{t^{2}} u^{5} d u