integral from-4 to 1 of (4-x^2-3x)

Lösung

\int_{- 4}^{1} (4 - x^{2} - 3 x) d x

\frac{125}{6}

Dezimale

20.83333 \dots

Schritte zur Lösung

\int_{- 4}^{1} 4 - 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_{- 4}^{1} 4 d x - \int_{- 4}^{1} x^{2} d x - \int_{- 4}^{1} 3 x d x

\int_{- 4}^{1} 4 d x = 20

\int_{- 4}^{1} x^{2} d x = \frac{65}{3}

\int_{- 4}^{1} 3 x d x = - \frac{45}{2}

= 20 - \frac{65}{3} - (- \frac{45}{2})

Vereinfache

20 - \frac{65}{3} - (- \frac{45}{2}) : \frac{125}{6}

= \frac{125}{6}