integral from 1 to 4 of-10sqrt(t)ln(t)

Lösung

\int_{1}^{4} - 10 t ln (t) d t

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

Dezimale

- 42.82458 \dots

Schritte zur Lösung

\int_{1}^{4} - 10 t ln (t) d t

Entferne die Konstante:

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

= - 10 \cdot \int_{1}^{4} t ln (t) d t

Wende die partielle Integration an

= - 10 [\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}}

= - 10 [\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)

= - 10 (- \frac{28}{9} + \frac{32}{3} ln (2))

\int 10 x^{5} e^{- x^{3}} d x

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