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

Lösung

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

\frac{441 21}{5} - 55 + 4 (721 - \frac{5 5}{3})

Dezimale

506.40783 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{5}^{21} (u^{2} + 4) u^{2} d u

Multipliziere aus

(u^{2} + 4) u^{2} : u^{4} + 4 u^{2}

= \int_{5}^{21} u^{4} + 4 u^{2} d u

Wende die Summenregel an:

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

= \int_{5}^{21} u^{4} d u + \int_{5}^{21} 4 u^{2} d u

\int_{5}^{21} u^{4} d u = \frac{441 21}{5} - 55

\int_{5}^{21} 4 u^{2} d u = 4 (721 - \frac{5 5}{3})

= \frac{441 21}{5} - 55 + 4 (721 - \frac{5 5}{3})

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