integral from-4 to 0 of-y-(y^2+3y)

Lösung

\int_{- 4}^{0} - y - (y^{2} + 3 y) d y

\frac{32}{3}

Dezimale

10.66666 \dots

Schritte zur Lösung

\int_{- 4}^{0} - y - (y^{2} + 3 y) d y

Vereinfache

= \int_{- 4}^{0} - y^{2} - 4 y d y

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{- 4}^{0} y^{2} d y - \int_{- 4}^{0} 4 y d y

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

\int_{- 4}^{0} 4 y d y = - 32

= - \frac{64}{3} - (- 32)

Vereinfache

- \frac{64}{3} - (- 32) : \frac{32}{3}

= \frac{32}{3}

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