integral from 0 to 12 of e^{-sqrt(x)}

Lösung

\int_{0}^{12} e^{- x} d x

- 2 (- 1 - \frac{- 2 3 - 1}{e ^{23}})

Dezimale

1.72053 \dots

Schritte zur Lösung

\int_{0}^{12} e^{- x} d x

Wende U-Substitution an

= \int_{0}^{- 23} 2 e^{u} u d u

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

= - \int_{- 23}^{0} 2 e^{u} u d u

Entferne die Konstante:

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

= - 2 \cdot \int_{- 23}^{0} e^{u} u d u

Wende die partielle Integration an

= - 2 [e^{u} u - \int e^{u} d u]_{- 23}^{0}

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

= - 2 [e^{u} u - e^{u}]_{- 23}^{0}

Berechne die Grenzen:

- 1 - \frac{- 2 3 - 1}{e ^{23}}

= - 2 (- 1 - \frac{- 2 3 - 1}{e ^{23}})

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