integral from-1 to 2 of e^{-3x}

Lösung

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

\frac{e ^{9} - 1}{3 e ^{6}}

Dezimale

6.69435 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{3}^{- 6} - \frac{1}{3} e^{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 6}^{3} - \frac{1}{3} e^{u} d u

Entferne die Konstante:

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

= - (- \frac{1}{3} \cdot \int_{- 6}^{3} e^{u} d u)

Nutze das gemeinsame Integral :

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

= - (- \frac{1}{3} [e^{u}]_{- 6}^{3})

Vereinfache

= \frac{1}{3} [e^{u}]_{- 6}^{3}

Berechne die Grenzen:

e^{3} - \frac{1}{e ^{6}}

= \frac{1}{3} (e^{3} - \frac{1}{e ^{6}})

Vereinfache

= \frac{e ^{9} - 1}{3 e ^{6}}

\int_{0}^{3} 3^{s} d s

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

\int_{0}^{1} \frac{x ^{2}}{( 1 + x ) ^{4}} d x

\int_{0}^{1} (\frac{x - 1}{x + 1}) d x

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