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Beliebt Rechnen >

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

Lösung

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

Lösung

- 1 + e^{x}

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{x}^{0} - e^{u} d u

Entferne die Konstante:

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

= - \int_{x}^{0} e^{u} d u

Nutze das gemeinsame Integral :

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

= - [e^{u}]_{x}^{0}

Berechne die Grenzen:

1 - e^{x}

= - (1 - e^{x})

Vereinfache

= - 1 + e^{x}

Beliebte Beispiele

integral from 0 to 2 of (x^2+3x-3)

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

integral from 2 to 8 of 8

\int_{2}^{8} 8 d x

integral from 1/2 to 1 of 3x

\int_{\frac{1}{2}}^{1} 3 x d x

integral from 0 to pi of (sin(x)+cos(x))

\int_{0}^{π} (sin (x) + cos (x)) d x

integral from 0 to 1 of 12x

\int_{0}^{1} 12 x d x