integral from-3 to 1 of 1/(x^{2/3)}

Lösung

\int_{- 3}^{1} \frac{1}{x ^{\frac{2}{3}}} d x

3 \cdot 3^{\frac{1}{3}} + 3

Dezimale

7.32674 \dots

Schritte zur Lösung

\int_{- 3}^{1} \frac{1}{x ^{\frac{2}{3}}} d x

Bestimme unbestimmte (Singularitäts-)Punkte:

x = 0

Wenn

b, a < b < c, f (b) =

unbestimmt

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 3}^{0} \frac{1}{x ^{\frac{2}{3}}} d x + \int_{0}^{1} \frac{1}{x ^{\frac{2}{3}}} d x

\int_{- 3}^{0} \frac{1}{x ^{\frac{2}{3}}} d x = - 3 (- 1)^{\frac{1}{3}} \cdot 3^{\frac{1}{3}}

\int_{0}^{1} \frac{1}{x ^{\frac{2}{3}}} d x = 3

= - 3 (- 1)^{\frac{1}{3}} \cdot 3^{\frac{1}{3}} + 3

Vereinfache

- 3 (- 1)^{\frac{1}{3}} \cdot 3^{\frac{1}{3}} + 3 : 3 \cdot 3^{\frac{1}{3}} + 3

= 3 \cdot 3^{\frac{1}{3}} + 3

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