integral from 0 to x of sqrt(x)cos(x)

Lösung

\int_{0}^{x} x cos (x) d x

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

Schritte zur Lösung

\int_{0}^{x} x cos (x) d x

Wende die partielle Integration an

= [x sin (x) - \int \frac{sin ( x )}{2 x} d x]_{0}^{x}

\int \frac{sin ( x )}{2 x} d x = \frac{π}{2} § (\frac{2}{π} x)

= [x sin (x) - \frac{π}{2} § (\frac{2}{π} x)]_{0}^{x}

Berechne die Grenzen:

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

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

\int_{1}^{2} ln (5 x) d x

\int_{- 5}^{2} \frac{x + 5}{x - 3} d x

\int_{2}^{6} ∣ x - 3 ∣ d x

\int_{0}^{π} 3 sin (2 x) d x

\int_{1}^{x} 2 y e^{- x} d y