integral from 0 to 5 of (4t-1)^2

Lösung

\int_{0}^{5} (4 t - 1)^{2} d t

\frac{1715}{3}

Dezimale

571.66666 \dots

Schritte zur Lösung

\int_{0}^{5} (4 t - 1)^{2} d t

Multipliziere aus

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

= \int_{0}^{5} 16 t^{2} - 8 t + 1 d t

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}^{5} 16 t^{2} d t - \int_{0}^{5} 8 t d t + \int_{0}^{5} 1 d t

\int_{0}^{5} 16 t^{2} d t = \frac{2000}{3}

\int_{0}^{5} 8 t d t = 100

\int_{0}^{5} 1 d t = 5

= \frac{2000}{3} - 100 + 5

Vereinfache

\frac{2000}{3} - 100 + 5 : \frac{1715}{3}

= \frac{1715}{3}

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