integral from 0 to 1 of x^2e^{6x}

Lösung

\int_{0}^{1} x^{2} e^{6 x} d x

\frac{13 e ^{6} - 1}{108}

Dezimale

48.55161 \dots

Schritte zur Lösung

\int_{0}^{1} x^{2} e^{6 x} d x

Wende die partielle Integration an

= [\frac{1}{6} e^{6 x} x^{2} - \int \frac{1}{3} e^{6 x} x d x]_{0}^{1}

\int \frac{1}{3} e^{6 x} x d x = \frac{1}{108} (6 e^{6 x} x - e^{6 x})

= [\frac{1}{6} e^{6 x} x^{2} - \frac{1}{108} (6 e^{6 x} x - e^{6 x})]_{0}^{1}

Berechne die Grenzen:

\frac{13 e ^{6}}{108} - \frac{1}{108}

= \frac{13 e ^{6}}{108} - \frac{1}{108}

Vereinfache

= \frac{13 e ^{6} - 1}{108}

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