integral from 0 to x^5 of sin(t^2)

Lösung

\int_{0}^{x^{5}} sin (t^{2}) d t

\frac{π}{2} § (\frac{2}{π} x^{5}) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

Schritte zur Lösung

\int_{0}^{x^{5}} 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)]_{0}^{x^{5}}

Berechne die Grenzen:

\frac{π}{2} § (\frac{2}{π} x^{5}) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

= \frac{π}{2} § (\frac{2}{π} x^{5}) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

\int_{0}^{\frac{π}{4}} 3 cos^{2} (x) d x

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\int_{- 2}^{1} 5 d x