integral from 1 to 2 of 4x^3e^{x^4}

Lösung

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

e^{16} - e

Dezimale

8886107.80222 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

= 4 \cdot \int_{1}^{2} x^{3} e^{x^{4}} d x

Wende U-Substitution an

= 4 \cdot \int_{1}^{8} \frac{e ^{u^{\frac{4}{3}}} u ^{\frac{1}{3}}}{3} d u

Entferne die Konstante:

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

= 4 \cdot \frac{1}{3} \cdot \int_{1}^{8} e^{u^{\frac{4}{3}}} u^{\frac{1}{3}} d u

Wende U-Substitution an

= 4 \cdot \frac{1}{3} \cdot \int_{1}^{16} \frac{3 e ^{v}}{4} d v

Entferne die Konstante:

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

= 4 \cdot \frac{1}{3} \cdot \frac{3}{4} \cdot \int_{1}^{16} e^{v} d v

Nutze das gemeinsame Integral :

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

= 4 \cdot \frac{1}{3} \cdot \frac{3}{4} [e^{v}]_{1}^{16}

Vereinfache

4 \cdot \frac{1}{3} \cdot \frac{3}{4} [e^{v}]_{1}^{16} : [e^{v}]_{1}^{16}

= [e^{v}]_{1}^{16}

Berechne die Grenzen:

e^{16} - e

= e^{16} - e

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