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

Lösung

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

\frac{10}{3}

Dezimale

3.33333 \dots

Schritte zur Lösung

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

Vereinfache

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

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 2 x d x = 4

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

= - \frac{8}{3} + 4 + 2

Vereinfache

- \frac{8}{3} + 4 + 2 : \frac{10}{3}

= \frac{10}{3}

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