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

Lösung

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

e^{4} - \frac{π}{4} erfi (2) - \frac{e}{2} + \frac{π}{4} erfi (1)

Schritte zur Lösung

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

Vereinfache

= \int_{1}^{2} e^{x^{2}} x^{2} d x

Vereinfache

x^{2} : xx

= \int_{1}^{2} e^{x^{2}} xx d x

Wende die partielle Integration an

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

\int \frac{1}{2} e^{x^{2}} d x = \frac{π}{4} erfi (x)

= [\frac{1}{2} e^{x^{2}} x - \frac{π}{4} erfi (x)]_{1}^{2}

Berechne die Grenzen:

e^{4} - \frac{π}{4} erfi (2) - \frac{e}{2} + \frac{π}{4} erfi (1)

= e^{4} - \frac{π}{4} erfi (2) - \frac{e}{2} + \frac{π}{4} erfi (1)

\int_{0}^{1} 3 x (x^{2} - 1)^{13} d x

\int_{x^{2}}^{2 x} 4 x y d y

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