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

Lösung

\int_{- 2}^{2} (e^{x + 2}) d x

e^{4} - 1

Dezimale

53.59815 \dots

Schritte zur Lösung

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

e^{x + 2} = e^{2} e^{x}

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

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

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

Vereinfache

= e^{4} - 1

\int_{0}^{3} e^{x} - 1 d x

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

\int_{0}^{1} (5 x^{2} - 8 x + 3) d x

\int_{5}^{13} (5 - x) (x - 13) d x

\int_{0}^{\infty} \frac{1}{3 ^{x}} d x