integral from x^2 to 4 of sqrt(y)cos(y)

Lösung

\int_{x^{2}}^{4} y cos (y) d y

2 sin (4) - \frac{π}{2} § (4 \frac{2}{π}) - x sin (x^{2}) + \frac{π}{2} § (\frac{2}{π} x^{2})

Schritte zur Lösung

\int_{x^{2}}^{4} y cos (y) d y

Wende die partielle Integration an

= [y sin (y) - \int \frac{sin ( y )}{2 y} d y]_{x^{2}}^{4}

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

= [y sin (y) - \frac{π}{2} § (\frac{2}{π} y)]_{x^{2}}^{4}

Berechne die Grenzen:

2 sin (4) - \frac{π}{2} § (4 \frac{2}{π}) - x sin (x^{2}) + \frac{π}{2} § (\frac{2}{π} x^{2})

= 2 sin (4) - \frac{π}{2} § (4 \frac{2}{π}) - x sin (x^{2}) + \frac{π}{2} § (\frac{2}{π} x^{2})

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