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

Lösung

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

\frac{855}{4}

Dezimale

213.75

Schritte zur Lösung

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

\int_{- 2}^{3} 2 x^{4} d x = 110

\int_{- 2}^{3} 5 x^{3} d x = \frac{325}{4}

\int_{- 2}^{3} x d x = \frac{5}{2}

\int_{- 2}^{3} 5 d x = 25

= 110 + \frac{325}{4} - \frac{5}{2} + 25

Vereinfache

110 + \frac{325}{4} - \frac{5}{2} + 25 : \frac{855}{4}

= \frac{855}{4}

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