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Beliebt Rechnen >

integral from 0 to 1 of (3e^{-x}-e^{-2x})

Lösung

\int_{0}^{1} (3 e^{- x} - e^{- 2 x}) d x

Lösung

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

+1

Dezimale

1.46402 \dots

Schritte zur Lösung

\int_{0}^{1} 3 e^{- x} - e^{- 2 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_{0}^{1} 3 e^{- x} d x - \int_{0}^{1} e^{- 2 x} d x

\int_{0}^{1} 3 e^{- x} d x = 3 (1 - \frac{1}{e})

\int_{0}^{1} e^{- 2 x} d x = \frac{e ^{2} - 1}{2 e ^{2}}

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

Graph

Beliebte Beispiele

y^{''}+6y^'+9y=27+e^{-3x}

y^{^{''}} + 6 y^{^{'}} + 9 y = 27 + e^{- 3 x}

integral of e^{3ln(4x-5)}

\int e^{3 l n (4 x - 5)} d x

f(x)=sqrt(5-3x)

f (x) = 5 - 3 x

y^{^{'}} - 1 = y^{2}

inverselaplace 2/(s(s^2+2s+2))

in v erse l a pl a ce \frac{2}{s ( s ^{2} + 2 s + 2 )}