integral from 0 to 2pi of cos(x^2)

Lösung

\int_{0}^{2 π} cos (x^{2}) d x

\frac{π}{2} C (\frac{2}{π} \cdot 2 π) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

Schritte zur Lösung

\int_{0}^{2 π} cos (x^{2}) d x

Das ist ein nicht elementares Integral :

\int cos (x^{2}) d x = \frac{π}{2} C (\frac{2}{π} x)

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

Berechne die Grenzen:

\frac{π}{2} C (\frac{2}{π} \cdot 2 π) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

= \frac{π}{2} C (\frac{2}{π} \cdot 2 π) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

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