integral from 2 to 5 of ((x^4+x^2))/3

Lösung

\int_{2}^{5} \frac{( x ^{4} + x ^{2} )}{3} d x

\frac{1096}{5}

Dezimale

219.2

Schritte zur Lösung

\int_{2}^{5} \frac{x ^{4} + x ^{2}}{3} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int_{2}^{5} x^{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

= \frac{1}{3} (\int_{2}^{5} x^{4} d x + \int_{2}^{5} x^{2} d x)

\int_{2}^{5} x^{4} d x = \frac{3093}{5}

\int_{2}^{5} x^{2} d x = 39

= \frac{1}{3} (\frac{3093}{5} + 39)

Vereinfache

\frac{1}{3} (\frac{3093}{5} + 39) : \frac{1096}{5}

= \frac{1096}{5}

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