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

Lösung

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

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

Dezimale

- 17.12983 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die partielle Integration an

= - 4 [\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}}

= - 4 [\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)

= - 4 (- \frac{28}{9} + \frac{32}{3} ln (2))

d er i v a t i v e sin (x^{4})

d er i v a t i v e y = 9^{5^{x^{2}}}

a re a y = 2, y = 2 sin (x), [0, \frac{π}{2}]

(e^{3 t})^{^{'}}

\int \frac{3 t ^{4} - t ^{3} + 6 t ^{2}}{t ^{4}} d t