integral from 0 to 2 of 2t*e^{t^2}

Lösung

\int_{0}^{2} 2 t \cdot e^{t^{2}} d t

e^{4} - 1

Dezimale

53.59815 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{2} t e^{t^{2}} d t

Wende U-Substitution an

= 2 \cdot \int_{0}^{4} \frac{e ^{u}}{2} d u

Entferne die Konstante:

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

= 2 \cdot \frac{1}{2} \cdot \int_{0}^{4} e^{u} d u

Nutze das gemeinsame Integral :

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

= 2 \cdot \frac{1}{2} [e^{u}]_{0}^{4}

Vereinfache

2 \cdot \frac{1}{2} [e^{u}]_{0}^{4} : [e^{u}]_{0}^{4}

= [e^{u}]_{0}^{4}

Berechne die Grenzen:

e^{4} - 1

= e^{4} - 1

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