integral from-1 to 0 of x/(sqrt(2+x))

Lösung

\int_{- 1}^{0} \frac{x}{2 + x} d x

2 (\frac{2 2 - 1}{3} - 22 + 2)

Dezimale

- 0.43790 \dots

Schritte zur Lösung

\int_{- 1}^{0} \frac{x}{2 + x} d x

Wende U-Substitution an

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{1}^{2} u^{2} - 2 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

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

\int_{1}^{2} u^{2} d u = \frac{2 2 - 1}{3}

\int_{1}^{2} 2 d u = 22 - 2

= 2 (\frac{2 2 - 1}{3} - (22 - 2))

Vereinfache

= 2 (\frac{2 2 - 1}{3} - 22 + 2)

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