integral from 8 to 0 of (2x^2+x+2)

Lösung

\int_{8}^{0} (2 x^{2} + x + 2) d x

- \frac{1168}{3}

Dezimale

- 389.33333 \dots

Schritte zur Lösung

\int_{8}^{0} 2 x^{2} + x + 2 d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{8} 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}^{8} 2 x^{2} d x + \int_{0}^{8} x d x + \int_{0}^{8} 2 d x)

\int_{0}^{8} 2 x^{2} d x = \frac{1024}{3}

\int_{0}^{8} x d x = 32

\int_{0}^{8} 2 d x = 16

= - (\frac{1024}{3} + 32 + 16)

Vereinfache

- (\frac{1024}{3} + 32 + 16) : - \frac{1168}{3}

= - \frac{1168}{3}

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