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

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

Commented by jagoll last updated on 16/Apr/20

$$\sqrt{x-4}=t\Rightarrow x=t^2+4$$$$dx=2tdt$$$$\underset{0}{\stackrel{1}{\int }}{(t^2+4)}^{2}t\left(2t\right)dt=$$$$\underset{0}{\stackrel{1}{\int }}2t^2(t^4+8t^2+16)dt=$$$$\underset{0}{\stackrel{1}{\int }}2t^6+16t^4+32t^{2}dt=$$$$\frac{2}{7}+\frac{16}{5}+\frac{32}{3}$$

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