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Beliebt Rechnen >

integral from 1 to 4 of e^{-x}

Lösung

\int_{1}^{4} e^{- x} d x

Lösung

\frac{1}{e} - \frac{1}{e ^{4}}

+1

Dezimale

0.34956 \dots

Schritte zur Lösung

\int_{1}^{4} e^{- x} d x

Wende U-Substitution an

= \int_{- 1}^{- 4} - e^{u} d u

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

= - \int_{- 4}^{- 1} - e^{u} d u

Entferne die Konstante:

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

= - (- \int_{- 4}^{- 1} e^{u} d u)

Nutze das gemeinsame Integral :

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

= - (- [e^{u}]_{- 4}^{- 1})

Vereinfache

= [e^{u}]_{- 4}^{- 1}

Berechne die Grenzen:

\frac{1}{e} - \frac{1}{e ^{4}}

= \frac{1}{e} - \frac{1}{e ^{4}}

Graph

Beliebte Beispiele

integral from-1 to 2 of-x^2

\int_{- 1}^{2} - x^{2} d x

integral from-2 to 2 of-x^2+5

\int_{- 2}^{2} - x^{2} + 5 d x

integral from 0 to 1 of 1/2 e^x+3/4 2^x

\int_{0}^{1} \frac{1}{2} e^{x} + \frac{3}{4} 2^{x} d x

integral from-3 to 7 of (|x|)

\int_{- 3}^{7} (∣ x ∣) d x

integral from 0 to pi/2 of sin(8x)

\int_{0}^{\frac{π}{2}} sin (8 x) d x