integral from-1 to 5 of 4x(1-x^2)

Lösung

\int_{- 1}^{5} 4 x (1 - x^{2}) d x

- 576

Schritte zur Lösung

\int_{- 1}^{5} 4 x (1 - x^{2}) d x

Entferne die Konstante:

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

= 4 \cdot \int_{- 1}^{5} x (1 - x^{2}) d x

Multipliziere aus

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

= 4 \cdot \int_{- 1}^{5} x - x^{3} 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

= 4 (\int_{- 1}^{5} x d x - \int_{- 1}^{5} x^{3} d x)

\int_{- 1}^{5} x d x = 12

\int_{- 1}^{5} x^{3} d x = 156

= 4 (12 - 156)

Vereinfache

= - 576

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

\int_{1}^{3} x e^{x} d x

\int_{0}^{\frac{π}{2}} sin (x) cos (2 x) d x

\int_{0}^{3} e^{5 x} d x

\int_{- 1}^{0} \frac{1}{x ^{2} - 25} d x