integral from 0 to 4 of (4x^3-9x^2+2x-1)

Lösung

\int_{0}^{4} (4 x^{3} - 9 x^{2} + 2 x - 1) d x

76

Schritte zur Lösung

\int_{0}^{4} 4 x^{3} - 9 x^{2} + 2 x - 1 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}^{4} 4 x^{3} d x - \int_{0}^{4} 9 x^{2} d x + \int_{0}^{4} 2 x d x - \int_{0}^{4} 1 d x

\int_{0}^{4} 4 x^{3} d x = 256

\int_{0}^{4} 9 x^{2} d x = 192

\int_{0}^{4} 2 x d x = 16

\int_{0}^{4} 1 d x = 4

= 256 - 192 + 16 - 4

Vereinfache

= 76

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

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

\int_{- 1}^{1} (x^{5} - x^{6}) d x

\int_{1}^{3} k x^{2} - 2 d x

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