integral from 1 to 3 of 15r^3ln(r)

Lösung

\int_{1}^{3} 15 r^{3} ln (r) d r

15 (- 5 + \frac{81}{4} ln (3))

Dezimale

258.70348 \dots

Schritte zur Lösung

\int_{1}^{3} 15 r^{3} ln (r) d r

Entferne die Konstante:

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

= 15 \cdot \int_{1}^{3} r^{3} ln (r) d r

Wende die partielle Integration an

= 15 [\frac{1}{4} r^{4} ln (r) - \int \frac{r ^{3}}{4} d r]_{1}^{3}

\int \frac{r ^{3}}{4} d r = \frac{r ^{4}}{16}

= 15 [\frac{1}{4} r^{4} ln (r) - \frac{r ^{4}}{16}]_{1}^{3}

Berechne die Grenzen:

- 5 + \frac{81}{4} ln (3)

= 15 (- 5 + \frac{81}{4} ln (3))

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