integral from 1 to 3 of (-x^3+6x^2+7x-5)

Lösung

\int_{1}^{3} (- x^{3} + 6 x^{2} + 7 x - 5) d x

50

Schritte zur Lösung

\int_{1}^{3} - x^{3} + 6 x^{2} + 7 x - 5 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_{1}^{3} x^{3} d x + \int_{1}^{3} 6 x^{2} d x + \int_{1}^{3} 7 x d x - \int_{1}^{3} 5 d x

\int_{1}^{3} x^{3} d x = 20

\int_{1}^{3} 6 x^{2} d x = 52

\int_{1}^{3} 7 x d x = 28

\int_{1}^{3} 5 d x = 10

= - 20 + 52 + 28 - 10

Vereinfache

= 50

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