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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{2 ( e ^{6} - 1 )}{3 e ^{6}}

+1

Dezimale

0.66501 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{2} e^{- 3 x} d x

Wende U-Substitution an

= 2 \cdot \int_{0}^{- 6} - \frac{1}{3} e^{u} d u

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

= 2 (- \int_{- 6}^{0} - \frac{1}{3} e^{u} d u)

Entferne die Konstante:

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

= 2 (- (- \frac{1}{3} \cdot \int_{- 6}^{0} e^{u} d u))

Nutze das gemeinsame Integral :

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

= 2 (- (- \frac{1}{3} [e^{u}]_{- 6}^{0}))

Vereinfache

2 (- (- \frac{1}{3} [e^{u}]_{- 6}^{0})) : \frac{2}{3} [e^{u}]_{- 6}^{0}

= \frac{2}{3} [e^{u}]_{- 6}^{0}

Berechne die Grenzen:

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

= \frac{2}{3} (1 - \frac{1}{e ^{6}})

Vereinfache

= \frac{2 ( e ^{6} - 1 )}{3 e ^{6}}

Graph

Beliebte Beispiele

derivative of (x^{1/3}-1^3)

\frac{d}{d x} ((x^{\frac{1}{3}} - 1)^{3})

xy^'=y+3x^2sin(x),y(pi)=0

x y^{^{'}} = y + 3 x^{2} sin (x), y (π) = 0

integral from 2 to 4 of 1/(x^2-25)

\int_{2}^{4} \frac{1}{x ^{2} - 25} d x

limit as x approaches 0 of (4x)^{7x}

x \to 0 lim ((4 x)^{7 x})

fläche-2x^2+x,-2,1

a re a - 2 x^{2} + x, - 2, 1