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

Lösung

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

- 4 (e - \frac{1}{e})

Dezimale

- 9.40160 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende U-Substitution an

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

Entferne die Konstante:

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

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

Nutze das gemeinsame Integral :

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

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

Berechne die Grenzen:

e - \frac{1}{e}

= - 4 (e - \frac{1}{e})

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