integral from 0 to x of x^2sin(t^2)

Lösung

\int_{0}^{x} x^{2} sin (t^{2}) d t

x^{2} (\frac{π}{2} § (\frac{2}{π} x) - \frac{π}{2} § (\frac{2}{π} \cdot 0))

Schritte zur Lösung

\int_{0}^{x} x^{2} sin (t^{2}) d t

Entferne die Konstante:

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

= x^{2} \cdot \int_{0}^{x} sin (t^{2}) d t

Das ist ein nicht elementares Integral :

\int sin (x^{2}) d x = \frac{π}{2} § (\frac{2}{π} x)

= x^{2} [\frac{π}{2} § (\frac{2}{π} t)]_{0}^{x}

Berechne die Grenzen:

\frac{π}{2} § (\frac{2}{π} x) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

= x^{2} (\frac{π}{2} § (\frac{2}{π} x) - \frac{π}{2} § (\frac{2}{π} \cdot 0))

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