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

Lösung

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

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

Schritte zur Lösung

\int_{0}^{x^{3}} 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^{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}^{5} x e^{- \frac{x}{4}} d x

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

\int_{1}^{\infty} \frac{1}{4 x - 1} d x

\int_{\frac{π}{2}}^{0} - sin^{2} (t) d t

\int_{0}^{1} x^{2} 7 x + 8 d x