integral from-3 to 1 of (e^{x+3})

Lösung

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

e^{4} - 1

Dezimale

53.59815 \dots

Schritte zur Lösung

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

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

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

Nutze das gemeinsame Integral :

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

= e^{3} [e^{x}]_{- 3}^{1}

Berechne die Grenzen:

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

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

Vereinfache

= e^{4} - 1

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

\int_{- 1}^{2} 4 t^{2} + 5 d t

\int_{0}^{2} 6 x (4 - x) d x

\int_{0}^{\frac{π}{18}} sin^{5} (9 x) d x

\int_{0}^{5} 2 x - 5 d x