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

Lösung

\int_{x}^{2 π} cos (t^{2}) d t

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

Schritte zur Lösung

\int_{x}^{2 π} cos (t^{2}) d t

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} t)]_{x}^{2 π}

Berechne die Grenzen:

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

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

\int_{0}^{1} x 5 x^{2} + 4 d x

\int_{0}^{1} x^{2} - x + 1 d x

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

\int_{0}^{1} 3 y^{2} d y

\int_{- 3}^{- 1} \frac{1}{x ^{2} - 6 x + 25} d x