integral from-3 to 2 of e^{x+3}

Lösung

\int_{- 3}^{2} e^{x + 3} d x

e^{5} - 1

Dezimale

147.41315 \dots

Schritte zur Lösung

\int_{- 3}^{2} e^{x + 3} d x

e^{x + 3} = e^{3} e^{x}

= \int_{- 3}^{2} e^{3} e^{x} d x

Entferne die Konstante:

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

= e^{3} \cdot \int_{- 3}^{2} e^{x} d x

Nutze das gemeinsame Integral :

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

= e^{3} [e^{x}]_{- 3}^{2}

Berechne die Grenzen:

e^{2} - \frac{1}{e ^{3}}

= e^{3} (e^{2} - \frac{1}{e ^{3}})

Vereinfache

= e^{5} - 1

\int_{0}^{4} \frac{x}{4} d x

\int_{- \infty}^{2} \frac{1}{x ^{2} + 4} d x

\int_{1}^{5} (2 x - 5)^{3} d x

\int_{0}^{1} \frac{1}{4 t} + 9 d t

\int_{1}^{2} e^{x} d x