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

Lösung

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

\frac{172}{3}

Dezimale

57.33333 \dots

Schritte zur Lösung

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

Multipliziere aus

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

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

\int_{0}^{4} 4 x^{2} d x = \frac{256}{3}

\int_{0}^{4} 4 x d x = 32

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

= \frac{256}{3} - 32 + 4

Vereinfache

\frac{256}{3} - 32 + 4 : \frac{172}{3}

= \frac{172}{3}

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