integral from 1 to 3 of x^3+2x^2-5x+2

Lösung

\int_{1}^{3} x^{3} + 2 x^{2} - 5 x + 2 d x

\frac{64}{3}

Dezimale

21.33333 \dots

Schritte zur Lösung

\int_{1}^{3} x^{3} + 2 x^{2} - 5 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_{1}^{3} x^{3} d x + \int_{1}^{3} 2 x^{2} d x - \int_{1}^{3} 5 x d x + \int_{1}^{3} 2 d x

\int_{1}^{3} x^{3} d x = 20

\int_{1}^{3} 2 x^{2} d x = \frac{52}{3}

\int_{1}^{3} 5 x d x = 20

\int_{1}^{3} 2 d x = 4

= 20 + \frac{52}{3} - 20 + 4

Vereinfache

20 + \frac{52}{3} - 20 + 4 : \frac{64}{3}

= \frac{64}{3}

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