integral from 1 to 2 of (x/y-y/x)

Lösung

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

x ln (2) - \frac{3}{2 x}

Schritte zur Lösung

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{1}^{2} \frac{x}{y} d y = x ln (2)

\int_{1}^{2} \frac{y}{x} d y = \frac{3}{2 x}

= x ln (2) - \frac{3}{2 x}

\int_{0}^{1} h (x - x^{2}) d x

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