4-5-x-2-x-4-

Question Number 89228 by cindiaulia last updated on 16/Apr/20

\underset{4}{\int^{5}} x^{2} \sqrt{x - 4}

Commented by jagoll last updated on 16/Apr/20

\sqrt{x - 4} = t \Rightarrow x = t^{2} + 4

d x = 2 t d t

\underset{0}{\int^{1}} {(t^{2} + 4)}^{2} t (2 t) d t =

\underset{0}{\int^{1}} 2 t^{2} (t^{4} + 8 t^{2} + 16) d t =

\underset{0}{\int^{1}} 2 t^{6} + 16 t^{4} + 32 t^{2} d t =

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

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