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

Lösung

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

8 ln (2) - \frac{9}{2}

Dezimale

1.04517 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{1}^{4} \frac{( u - 2 ) ^{2}}{u} d u

Multipliziere aus

\frac{( u - 2 ) ^{2}}{u} : u - 4 + \frac{4}{u}

= \int_{1}^{4} u - 4 + \frac{4}{u} d u

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} u d u - \int_{1}^{4} 4 d u + \int_{1}^{4} \frac{4}{u} d u

\int_{1}^{4} u d u = \frac{15}{2}

\int_{1}^{4} 4 d u = 12

\int_{1}^{4} \frac{4}{u} d u = 8 ln (2)

= \frac{15}{2} - 12 + 8 ln (2)

Ziehe Brüche zusammen

- 12 + \frac{15}{2} : - \frac{9}{2}

= 8 ln (2) - \frac{9}{2}

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