integral from-1 to 3 of x(x-1)(x+2)

Lösung

\int_{- 1}^{3} x (x - 1) (x + 2) d x

\frac{64}{3}

Dezimale

21.33333 \dots

Schritte zur Lösung

\int_{- 1}^{3} x (x - 1) (x + 2) d x

Wende die partielle Integration an

= [\frac{1}{6} (2 x^{4} + x^{3} - 6 x^{2} - 6 \cdot \int \frac{x ^{3}}{3} - \frac{x ^{2}}{2} d x)]_{- 1}^{3}

\int \frac{x ^{3}}{3} - \frac{x ^{2}}{2} d x = \frac{x ^{4}}{12} - \frac{x ^{3}}{6}

= [\frac{1}{6} (2 x^{4} + x^{3} - 6 x^{2} - 6 (\frac{x ^{4}}{12} - \frac{x ^{3}}{6}))]_{- 1}^{3}

Vereinfache

[\frac{1}{6} (2 x^{4} + x^{3} - 6 x^{2} - 6 (\frac{x ^{4}}{12} - \frac{x ^{3}}{6}))]_{- 1}^{3} : [\frac{1}{12} (3 x^{4} + 4 x^{3} - 12 x^{2})]_{- 1}^{3}

= [\frac{1}{12} (3 x^{4} + 4 x^{3} - 12 x^{2})]_{- 1}^{3}

Berechne die Grenzen:

\frac{64}{3}

= \frac{64}{3}

\int x^{3} x^{2} + 19 d x

t an g e n t y = \frac{4}{5 x + 1}, (- 1, - 1)

d er i v a t i v e \frac{9}{x ^{2}} - \frac{3}{x}

\frac{d}{d x} (2 e^{- x^{3}})

\int - \frac{1}{v ^{2}} d v