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Beliebt Rechnen >

integral from 1 to 4 of 6sqrt(t)ln(t)

Lösung

\int_{1}^{4} 6 t ln (t) d t

Lösung

6 (- \frac{28}{9} + \frac{32}{3} ln (2))

+1

Dezimale

25.69475 \dots

Schritte zur Lösung

\int_{1}^{4} 6 t ln (t) d t

Entferne die Konstante:

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

= 6 \cdot \int_{1}^{4} t ln (t) d t

Wende die partielle Integration an

= 6 [\frac{2}{3} t^{\frac{3}{2}} ln (t) - \int \frac{2}{3} t^{\frac{1}{2}} d t]_{1}^{4}

\int \frac{2}{3} t^{\frac{1}{2}} d t = \frac{4}{9} t^{\frac{3}{2}}

= 6 [\frac{2}{3} t^{\frac{3}{2}} ln (t) - \frac{4}{9} t^{\frac{3}{2}}]_{1}^{4}

Berechne die Grenzen:

- \frac{28}{9} + \frac{32}{3} ln (2)

= 6 (- \frac{28}{9} + \frac{32}{3} ln (2))

Graph

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