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

Lösung

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

111

Schritte zur Lösung

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

Multipliziere aus

(4 x - 1)^{2} : 16 x^{2} - 8 x + 1

= \int_{0}^{3} 16 x^{2} - 8 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}^{3} 16 x^{2} d x - \int_{0}^{3} 8 x d x + \int_{0}^{3} 1 d x

\int_{0}^{3} 16 x^{2} d x = 144

\int_{0}^{3} 8 x d x = 36

\int_{0}^{3} 1 d x = 3

= 144 - 36 + 3

Vereinfache

= 111

\int_{0}^{1} x^{\frac{5}{2}} d x

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