integral from-3 to 2 of (9-x^2)-(x+3)

Lösung

\int_{- 3}^{2} (9 - x^{2}) - (x + 3) d x

\frac{125}{6}

Dezimale

20.83333 \dots

Schritte zur Lösung

\int_{- 3}^{2} 9 - x^{2} - (x + 3) d x

Vereinfache

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

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

\int_{- 3}^{2} x d x = - \frac{5}{2}

\int_{- 3}^{2} 6 d x = 30

= - \frac{35}{3} - (- \frac{5}{2}) + 30

Vereinfache

- \frac{35}{3} - (- \frac{5}{2}) + 30 : \frac{125}{6}

= \frac{125}{6}

\int_{- 1}^{3} 3 x^{2} - 6 x - 9 d x

\int_{0}^{5} 1 + \frac{9}{4} x d x

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

\int_{0}^{2 π} - sin (t) d t

\int_{1}^{0} 1