integral from x to x^3 of sin(t^2)

Lösung

\int_{x}^{x^{3}} sin (t^{2}) d t

\frac{π}{2} § (\frac{2}{π} x^{3}) - \frac{π}{2} § (\frac{2}{π} x)

Schritte zur Lösung

\int_{x}^{x^{3}} 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)]_{x}^{x^{3}}

Berechne die Grenzen:

\frac{π}{2} § (\frac{2}{π} x^{3}) - \frac{π}{2} § (\frac{2}{π} x)

= \frac{π}{2} § (\frac{2}{π} x^{3}) - \frac{π}{2} § (\frac{2}{π} x)

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

\int_{0}^{\frac{1}{2}} 3 x^{2} d x

\int_{0}^{2} x^{2} 1 + 4 x^{2} d x

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

\int_{1}^{3} 6 x^{2} - 4 x + 5 d x