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

Lösung

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

- \frac{16}{3}

Dezimale

- 5.33333 \dots

Schritte zur Lösung

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

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

= - \int_{- 2}^{0} 4 - 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_{- 2}^{0} 4 d x - \int_{- 2}^{0} x^{2} d x)

\int_{- 2}^{0} 4 d x = 8

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

= - (8 - \frac{8}{3})

Füge

8 - \frac{8}{3}

zusammen:

\frac{16}{3}

= - \frac{16}{3}

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