integral from 2 to 0 of x^3-3x^2+2

Lösung

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

0

Schritte zur Lösung

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

\int_{0}^{2} x^{3} d x = 4

\int_{0}^{2} 3 x^{2} d x = 8

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

= - (4 - 8 + 4)

Vereinfache

= 0

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

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