integral from 0 to 2 of (8x-1)^2

Lösung

\int_{0}^{2} (8 x - 1)^{2} d x

\frac{422}{3}

Dezimale

140.66666 \dots

Schritte zur Lösung

\int_{0}^{2} (8 x - 1)^{2} d x

Multipliziere aus

(8 x - 1)^{2} : 64 x^{2} - 16 x + 1

= \int_{0}^{2} 64 x^{2} - 16 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}^{2} 64 x^{2} d x - \int_{0}^{2} 16 x d x + \int_{0}^{2} 1 d x

\int_{0}^{2} 64 x^{2} d x = \frac{512}{3}

\int_{0}^{2} 16 x d x = 32

\int_{0}^{2} 1 d x = 2

= \frac{512}{3} - 32 + 2

Vereinfache

\frac{512}{3} - 32 + 2 : \frac{422}{3}

= \frac{422}{3}