integral from 0 to 3 of (6x-x^2)-x^2

Lösung

\int_{0}^{3} (6 x - x^{2}) - x^{2} d x

9

Schritte zur Lösung

\int_{0}^{3} 6 x - x^{2} - x^{2} d x

Vereinfache

= \int_{0}^{3} 6 x - 2 x^{2} 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}^{3} 6 x d x - \int_{0}^{3} 2 x^{2} d x

\int_{0}^{3} 6 x d x = 27

\int_{0}^{3} 2 x^{2} d x = 18

= 27 - 18

Vereinfache

= 9

\int_{- 10}^{10} x d x

\int_{0}^{3} \frac{1}{2} x d x

\int_{0}^{8} (3 x)^{2} d x

\int_{- 3}^{3} x^{3} + \frac{1}{x} d x

\int_{0}^{\frac{1}{4}} y arctan (4 y) d y