integral from 0 to 4 of (1+3y-y^2)

Lösung

\int_{0}^{4} (1 + 3 y - y^{2}) d y

\frac{20}{3}

Dezimale

6.66666 \dots

Schritte zur Lösung

\int_{0}^{4} 1 + 3 y - y^{2} 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_{0}^{4} 1 d y + \int_{0}^{4} 3 y d y - \int_{0}^{4} y^{2} d y

\int_{0}^{4} 1 d y = 4

\int_{0}^{4} 3 y d y = 24

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

= 4 + 24 - \frac{64}{3}

Vereinfache

4 + 24 - \frac{64}{3} : \frac{20}{3}

= \frac{20}{3}

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