integral from y^2 to 4 of ycos(x^2)

Lösung

\int_{y^{2}}^{4} y cos (x^{2}) d x

y (\frac{π}{2} C (\frac{2}{π} \cdot 4) - \frac{π}{2} C (\frac{2}{π} y^{2}))

Schritte zur Lösung

\int_{y^{2}}^{4} y cos (x^{2}) d x

Entferne die Konstante:

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

= y \cdot \int_{y^{2}}^{4} 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)

= y [\frac{π}{2} C (\frac{2}{π} x)]_{y^{2}}^{4}

Berechne die Grenzen:

\frac{π}{2} C (\frac{2}{π} \cdot 4) - \frac{π}{2} C (\frac{2}{π} y^{2})

= y (\frac{π}{2} C (\frac{2}{π} \cdot 4) - \frac{π}{2} C (\frac{2}{π} y^{2}))

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