integral from 1 to 4 of e^{-x}x-e^{-x}

Lösung

\int_{1}^{4} e^{- x} x - e^{- x} d x

\frac{e ^{3} - 4}{e ^{4}}

Dezimale

0.29461 \dots

Schritte zur Lösung

\int_{1}^{4} e^{- x} x - e^{- x} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{4} e^{- x} x d x - \int_{1}^{4} e^{- x} d x

\int_{1}^{4} e^{- x} x d x = - \frac{5}{e ^{4}} + \frac{2}{e}

\int_{1}^{4} e^{- x} d x = \frac{1}{e} - \frac{1}{e ^{4}}

= - \frac{5}{e ^{4}} + \frac{2}{e} - (\frac{1}{e} - \frac{1}{e ^{4}})

Vereinfache

- \frac{5}{e ^{4}} + \frac{2}{e} - (\frac{1}{e} - \frac{1}{e ^{4}}) : \frac{e ^{3} - 4}{e ^{4}}

= \frac{e ^{3} - 4}{e ^{4}}

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