integral from 0 to x^3 of sin(t^2)

Lösung

\int_{0}^{x^{3}} sin (t^{2}) d t

\frac{π}{2} § (\frac{2}{π} x^{3}) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

Schritte zur Lösung

\int_{0}^{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)]_{0}^{x^{3}}

Berechne die Grenzen:

\frac{π}{2} § (\frac{2}{π} x^{3}) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

= \frac{π}{2} § (\frac{2}{π} x^{3}) - \frac{π}{2} § (\frac{2}{π} \cdot 0)

\int_{0}^{4} 2^{\frac{x}{2}} d x

\int_{- 2}^{2} (x^{3} - 4 x) d x

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

\int_{2}^{3} 4 x d x

\int_{0}^{1} \frac{y}{1 + x y} d x