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

Lösung

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

\frac{8}{3}

Dezimale

2.66666 \dots

Schritte zur Lösung

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

Multipliziere aus

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

= \int_{1}^{3} x^{2} - 2 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_{1}^{3} x^{2} d x - \int_{1}^{3} 2 x d x + \int_{1}^{3} 1 d x

\int_{1}^{3} x^{2} d x = \frac{26}{3}

\int_{1}^{3} 2 x d x = 8

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

= \frac{26}{3} - 8 + 2

Vereinfache

\frac{26}{3} - 8 + 2 : \frac{8}{3}

= \frac{8}{3}

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

\int_{0}^{1} 10 x d x

\int_{0}^{3} r^{3} d r

\int_{0}^{1} \frac{x}{3 x + 1} d x

\int_{- 2}^{- 1} \frac{1}{z} (y + \frac{1}{2}) d y