integral from 0 to 1 of cos(y^2)

Lösung

\int_{0}^{1} cos (y^{2}) d y

\frac{π}{2} C (\frac{2}{π} \cdot 1) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

Schritte zur Lösung

\int_{0}^{1} cos (y^{2}) d y

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} y)]_{0}^{1}

Berechne die Grenzen:

\frac{π}{2} C (\frac{2}{π} \cdot 1) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

= \frac{π}{2} C (\frac{2}{π} \cdot 1) - \frac{π}{2} C (\frac{2}{π} \cdot 0)

\int_{2}^{\infty} \frac{x}{x ^{2} - 1} d x

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

\int_{x^{2}}^{2 x} (x^{2} + y^{2}) d y

\int_{0}^{1} (x - 3)^{2} d x

\int_{1}^{2} \frac{x ^{2}}{x ^{3} + 1} d x