integral from 0 to 7 of x^3-9x^2+20x

Lösung

\int_{0}^{7} x^{3} - 9 x^{2} + 20 x d x

\frac{245}{4}

Dezimale

61.25

Schritte zur Lösung

\int_{0}^{7} x^{3} - 9 x^{2} + 20 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_{0}^{7} x^{3} d x - \int_{0}^{7} 9 x^{2} d x + \int_{0}^{7} 20 x d x

\int_{0}^{7} x^{3} d x = \frac{2401}{4}

\int_{0}^{7} 9 x^{2} d x = 1029

\int_{0}^{7} 20 x d x = 490

= \frac{2401}{4} - 1029 + 490

Vereinfache

\frac{2401}{4} - 1029 + 490 : \frac{245}{4}

= \frac{245}{4}

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

\int_{0}^{5} 15 x x + 4 d x

\int_{0}^{310} x^{2} d x

\int_{- 1}^{1} (- 30 x^{2} + 4 x y) d y

\int_{0}^{5} t^{2} + 2 t - 15 d t