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

Lösung

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

\frac{3}{10}

Dezimale

0.3

Schritte zur Lösung

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

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

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

\int_{1}^{2} (x - 1)^{4} d x = \frac{1}{5}

= \frac{3}{2} - 1 - \frac{1}{5}

Vereinfache

\frac{3}{2} - 1 - \frac{1}{5} : \frac{3}{10}

= \frac{3}{10}

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