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Beliebt Rechnen >

integral from 1 to 2 of 8r^2ln(r)

Lösung

\int_{1}^{2} 8 r^{2} ln (r) d r

Lösung

8 (- \frac{7}{9} + \frac{8}{3} ln (2))

+1

Dezimale

8.56491 \dots

Schritte zur Lösung

\int_{1}^{2} 8 r^{2} ln (r) d r

Entferne die Konstante:

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

= 8 \cdot \int_{1}^{2} r^{2} ln (r) d r

Wende die partielle Integration an

= 8 [\frac{1}{3} r^{3} ln (r) - \int \frac{r ^{2}}{3} d r]_{1}^{2}

\int \frac{r ^{2}}{3} d r = \frac{r ^{3}}{9}

= 8 [\frac{1}{3} r^{3} ln (r) - \frac{r ^{3}}{9}]_{1}^{2}

Berechne die Grenzen:

- \frac{7}{9} + \frac{8}{3} ln (2)

= 8 (- \frac{7}{9} + \frac{8}{3} ln (2))

Graph

Beliebte Beispiele

integral of 3t+2

\int 3 t + 2 d t

tangent f(x)=(x^3)/3-3/(x^3),\at x=-1

t an g e n t f (x) = \frac{x ^{3}}{3} - \frac{3}{x ^{3}}, at x = - 1

derivative f(x)=((2x)/7+1)

d er i v a t i v e f (x) = (\frac{2 x}{7} + 1)

integral of x^2sin^2(x)

\int x^{2} sin^{2} (x) d x

limit as x approaches 2-of x+1

x \to 2 - lim (x + 1)