integral from 1 to 4 of (x-3)/x

Lösung

\int_{1}^{4} \frac{x - 3}{x} d x

3 - 6 ln (2)

Dezimale

- 1.15888 \dots

Schritte zur Lösung

\int_{1}^{4} \frac{x - 3}{x} d x

Multipliziere aus

\frac{x - 3}{x} : 1 - \frac{3}{x}

= \int_{1}^{4} 1 - \frac{3}{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}^{4} 1 d x - \int_{1}^{4} \frac{3}{x} d x

\int_{1}^{4} 1 d x = 3

\int_{1}^{4} \frac{3}{x} d x = 6 ln (2)

= 3 - 6 ln (2)

\int_{1}^{3} 7 e^{x + 2} d x

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\int_{0}^{1} \frac{7}{( 3 x + 4 ) ( 5 x + 2 )} d x