integral from 1 to 9 of (x-4)/(sqrt(x))

Lösung

\int_{1}^{9} \frac{x - 4}{x} d x

\frac{4}{3}

Dezimale

1.33333 \dots

Schritte zur Lösung

\int_{1}^{9} \frac{x - 4}{x} d x

Multipliziere aus

\frac{x - 4}{x} : x - \frac{4}{x}

= \int_{1}^{9} x - \frac{4}{x} d x

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}^{9} x d x - \int_{1}^{9} \frac{4}{x} d x

\int_{1}^{9} x d x = \frac{52}{3}

\int_{1}^{9} \frac{4}{x} d x = 16

= \frac{52}{3} - 16

Vereinfache

\frac{52}{3} - 16 : \frac{4}{3}

= \frac{4}{3}

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