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

Lösung

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

\frac{32}{3}

Dezimale

10.66666 \dots

Schritte zur Lösung

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

Multipliziere aus

x (x - 1) (x + 3) : x^{3} + 2 x^{2} - 3 x

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int_{- 3}^{1} x^{3} d x = - 20

\int_{- 3}^{1} 2 x^{2} d x = \frac{56}{3}

\int_{- 3}^{1} 3 x d x = - 12

= - 20 + \frac{56}{3} - (- 12)

Vereinfache

- 20 + \frac{56}{3} - (- 12) : \frac{32}{3}

= \frac{32}{3}

\int_{0}^{x} x^{2} e^{- x} d x

\int_{0}^{1} (x e^{- x}) d x

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

\int_{0}^{2} 5^{2 x - 1} - 2^{3 x} d x

\int_{0}^{2} e^{- r^{2}} d r