integral from-1 to 3 of 1/(\sqrt[3]{x)}

Lösung

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

- \frac{3}{2} + \frac{3 \cdot 3 ^{\frac{2}{3}}}{2}

Dezimale

1.62012 \dots

Schritte zur Lösung

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

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

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

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

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

= - \frac{3}{2} + \frac{3 \cdot 3 ^{\frac{2}{3}}}{2}

\int_{1}^{4} 3 x^{2} + x d x

\int_{0}^{2} 2 t 4 t^{2} + 1 d t

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

\int_{4}^{5} (2 + 2 x)^{2} d x

\int_{0}^{\infty} x^{n} d x