integral from 0 to pi of 1/2 sin(x^2)

Lösung

\int_{0}^{π} \frac{1}{2} sin (x^{2}) d x

\frac{1}{2} (\frac{π}{2} § (\frac{2}{π} π) - \frac{π}{2} § (\frac{2}{π} \cdot 0))

Schritte zur Lösung

\int_{0}^{π} \frac{1}{2} sin (x^{2}) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{0}^{π} 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{1}{2} [\frac{π}{2} § (\frac{2}{π} x)]_{0}^{π}

Berechne die Grenzen:

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

= \frac{1}{2} (\frac{π}{2} § (\frac{2}{π} π) - \frac{π}{2} § (\frac{2}{π} \cdot 0))

\int_{- 2}^{3} x^{3} - 6 x d x

\int_{2}^{7} \frac{1}{x + 2 + 1} d x

\int_{0}^{\frac{π}{3}} x cos (x) d x

\int_{0}^{2 π} - cos (θ) d θ

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