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Beliebt Rechnen >

integral from 0 to 4 of pie^{-x/2}

Lösung

\int_{0}^{4} π e^{- \frac{x}{2}} d x

Lösung

2 π (1 - \frac{1}{e ^{2}})

+1

Dezimale

5.43284 \dots

Schritte zur Lösung

\int_{0}^{4} π e^{- \frac{x}{2}} d x

Entferne die Konstante:

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

= π \cdot \int_{0}^{4} e^{- \frac{x}{2}} d x

Wende U-Substitution an

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

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

= π (- \int_{- 2}^{0} - 2 e^{u} d u)

Entferne die Konstante:

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

= π (- (- 2 \cdot \int_{- 2}^{0} e^{u} d u))

Nutze das gemeinsame Integral :

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

= π (- (- 2 [e^{u}]_{- 2}^{0}))

Vereinfache

= 2 π [e^{u}]_{- 2}^{0}

Berechne die Grenzen:

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

= 2 π (1 - \frac{1}{e ^{2}})

Graph

Beliebte Beispiele

limit as x approaches 0 of 2^{(x-1)}

x \to 0 lim (2^{(x - 1)})

inverselaplace 4/(s+5)

in v erse l a pl a ce \frac{4}{s + 5}

derivative of-4e^xsin(x)

\frac{d}{d x} (- 4 e^{x} sin (x))

integral of 1/(x^4sqrt(16-25x^2))

\int \frac{1}{x ^{4} 16 - 25 x ^{2}} d x

derivative of (x^2-16/(x+4))

\frac{d}{d x} (\frac{x ^{2} - 16}{x + 4})