integral from 1 to 2 of (x+2/x)^2

Lösung

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

\frac{25}{3}

Dezimale

8.33333 \dots

Schritte zur Lösung

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

Multipliziere aus

(x + \frac{2}{x})^{2} : x^{2} + 4 + \frac{4}{x ^{2}}

= \int_{1}^{2} x^{2} + 4 + \frac{4}{x ^{2}} 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}^{2} x^{2} d x + \int_{1}^{2} 4 d x + \int_{1}^{2} \frac{4}{x ^{2}} d x

\int_{1}^{2} x^{2} d x = \frac{7}{3}

\int_{1}^{2} 4 d x = 4

\int_{1}^{2} \frac{4}{x ^{2}} d x = 2

= \frac{7}{3} + 4 + 2

Vereinfache

\frac{7}{3} + 4 + 2 : \frac{25}{3}

= \frac{25}{3}