integral from sqrt(x) to 3pi of cos(x^2)

Lösung

\int_{x}^{3 π} cos (x^{2}) d x

\frac{π}{2} C (\frac{2}{π} \cdot 3 π) - \frac{π}{2} C (\frac{2}{π} x)

Schritte zur Lösung

\int_{x}^{3 π} cos (x^{2}) d x

Das ist ein nicht elementares Integral :

\int cos (x^{2}) d x = \frac{π}{2} C (\frac{2}{π} x)

= [\frac{π}{2} C (\frac{2}{π} x)]_{x}^{3 π}

Berechne die Grenzen:

\frac{π}{2} C (\frac{2}{π} \cdot 3 π) - \frac{π}{2} C (\frac{2}{π} x)

= \frac{π}{2} C (\frac{2}{π} \cdot 3 π) - \frac{π}{2} C (\frac{2}{π} x)

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

\int_{1}^{2} - \frac{2}{x ^{2}} d x

\int_{0}^{\frac{2 π}{3}} cos (2 t) d t

\int_{e}^{e^{2}} (\frac{ln ( x )}{x}) d x

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