integral from 4 to 5 of x^2sqrt(x-4)

Lösung

\int_{4}^{5} x^{2} x - 4 d x

\frac{1486}{105}

Dezimale

14.15238 \dots

Schritte zur Lösung

\int_{4}^{5} x^{2} x - 4 d x

Wende U-Substitution an

= \int_{0}^{1} (u + 4)^{2} u d u

Multipliziere aus

(u + 4)^{2} u : u^{\frac{5}{2}} + 8 u^{\frac{3}{2}} + 16 u

= \int_{0}^{1} u^{\frac{5}{2}} + 8 u^{\frac{3}{2}} + 16 u d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} u^{\frac{5}{2}} d u + \int_{0}^{1} 8 u^{\frac{3}{2}} d u + \int_{0}^{1} 16 u d u

\int_{0}^{1} u^{\frac{5}{2}} d u = \frac{2}{7}

\int_{0}^{1} 8 u^{\frac{3}{2}} d u = \frac{16}{5}

\int_{0}^{1} 16 u d u = \frac{32}{3}

= \frac{2}{7} + \frac{16}{5} + \frac{32}{3}

Vereinfache

\frac{2}{7} + \frac{16}{5} + \frac{32}{3} : \frac{1486}{105}

= \frac{1486}{105}

\frac{\partial}{\partial t} (\frac{8.31 t}{V ( t )})

x \to 2 lim (\frac{2 x - 6}{x - 1})

x \to 9 - lim (\frac{5 x}{x - 9})

\frac{d}{d x} (- 4 x^{4} + 8 x^{3})

in v erse l a pl a ce \frac{( 3 s + 1 )}{s ( s + 2 )}