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

Lösung

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

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

Schritte zur Lösung

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

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} x)]_{0}^{x}

Berechne die Grenzen:

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

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

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

\int_{\frac{π}{2}}^{0} cos (x) d x

\int_{1}^{2} \frac{1}{x ( 1 + x ^{4} )} d x

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

\int_{0}^{\frac{π}{3}} sec (θ) tan (θ) d θ