integral from 0 to 1 of (x^3-2x^2+x+2)

Lösung

\int_{0}^{1} (x^{3} - 2 x^{2} + x + 2) d x

\frac{25}{12}

Dezimale

2.08333 \dots

Schritte zur Lösung

\int_{0}^{1} x^{3} - 2 x^{2} + x + 2 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}^{1} x^{3} d x - \int_{0}^{1} 2 x^{2} d x + \int_{0}^{1} x d x + \int_{0}^{1} 2 d x

\int_{0}^{1} x^{3} d x = \frac{1}{4}

\int_{0}^{1} 2 x^{2} d x = \frac{2}{3}

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

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

= \frac{1}{4} - \frac{2}{3} + \frac{1}{2} + 2

Vereinfache

\frac{1}{4} - \frac{2}{3} + \frac{1}{2} + 2 : \frac{25}{12}

= \frac{25}{12}

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