integral from 0 to 4 of-x^2+2x+3

Lösung

\int_{0}^{4} - x^{2} + 2 x + 3 d x

\frac{20}{3}

Dezimale

6.66666 \dots

Schritte zur Lösung

\int_{0}^{4} - x^{2} + 2 x + 3 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}^{4} x^{2} d x + \int_{0}^{4} 2 x d x + \int_{0}^{4} 3 d x

\int_{0}^{4} x^{2} d x = \frac{64}{3}

\int_{0}^{4} 2 x d x = 16

\int_{0}^{4} 3 d x = 12

= - \frac{64}{3} + 16 + 12

Vereinfache

- \frac{64}{3} + 16 + 12 : \frac{20}{3}

= \frac{20}{3}

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