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

Lösung

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

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

Schritte zur Lösung

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

Das ist ein nicht elementares Integral :

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

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

Berechne die Grenzen:

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

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

\int_{0}^{7} (7 x - x^{2}) d x

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\int_{0}^{3} \frac{1}{x - 3} d x

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\int_{1}^{2} 15 x^{2} (x^{3} - 7)^{4} d x