integral from-3 to 2 of x^3+x^2-6x

Lösung

\int_{- 3}^{2} x^{3} + x^{2} - 6 x d x

\frac{125}{12}

Dezimale

10.41666 \dots

Schritte zur Lösung

\int_{- 3}^{2} x^{3} + x^{2} - 6 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}^{2} x^{3} d x + \int_{- 3}^{2} x^{2} d x - \int_{- 3}^{2} 6 x d x

\int_{- 3}^{2} x^{3} d x = - \frac{65}{4}

\int_{- 3}^{2} x^{2} d x = \frac{35}{3}

\int_{- 3}^{2} 6 x d x = - 15

= - \frac{65}{4} + \frac{35}{3} - (- 15)

Vereinfache

- \frac{65}{4} + \frac{35}{3} - (- 15) : \frac{125}{12}

= \frac{125}{12}

\int_{1}^{8} \frac{2}{x} d x

\int_{x}^{1} (1 - y) cos^{2} (z - y) d z

\int_{0}^{π} \frac{1}{2} (2 θ)^{2} d θ

\int_{1}^{9} \frac{3}{t} d t

\int_{0}^{2} 4 + x d x