integral from-2 to 1 of e^{x+2}

Lösung

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

e^{3} - 1

Dezimale

19.08553 \dots

Schritte zur Lösung

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

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

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

Nutze das gemeinsame Integral :

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

= e^{2} [e^{x}]_{- 2}^{1}

Berechne die Grenzen:

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

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

Vereinfache

= e^{3} - 1

\int_{0}^{π} sin (n x) sin (x) d x

\int_{0}^{9} ∣ x - 6 ∣ d x

\int_{0}^{\frac{π}{4}} sec (t) tan (t) d t

\int_{- 2}^{0} 2 x x^{2} + 9 d x

\int_{- 2}^{0} (2 + x^{2}) d x