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

Lösung

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

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

Schritte zur Lösung

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

Berechne die Grenzen:

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

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

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

\int_{1}^{2} \frac{2}{9 + 4 x ^{2}} d x

\int_{1}^{3} 8 d x

\int_{0}^{\frac{π}{2}} cos (2 x - \frac{π}{2}) d x

\int_{0}^{1} r d r