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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

= - \frac{1}{2} [e^{u}]_{0}^{- 2 t}

Berechne die Grenzen:

e^{- 2 t} - 1

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

Beliebte Beispiele

integral of e^{-st}(t-2)^2

\int e^{- s t} (t - 2)^{2} d t

integral from x to y of (t^2-1)

\int_{x}^{y} (t^{2} - 1) d t

f^'(x)=x^{-3}+pix^2-sqrt(2)

f^{^{'}} (x) = x^{- 3} + π x^{2} - 2

derivative f(2)=10-3x

d er i v a t i v e f (2) = 10 - 3 x

limit as x approaches 2+of 2x

x \to 2 + lim (2 x)