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Question Number 70571 by ahmadshahhimat775@gmail.com last updated on 05/Oct/19

Commented by mathmax by abdo last updated on 05/Oct/19

$$\mathrm{\exists }c\in ]3,3+h[/{\int }_3^{h+3}\frac{5dx}{x^3+7}=\frac{5}{c^3+7}{\int }_3^{h+3}dx=\frac{5h}{c^3+7}\Rightarrow$$$$\frac{1}{h}{\int }_3^{h+3}\frac{5dx}{x^3+7}=\frac{5}{c^3+7}h\to 0\Rightarrow c\to 3\Rightarrow$$$${lim}_{h\to 0}\frac{1}{h}{\int }_3^{h+3}\frac{5dx}{x^3+7}=\frac{5}{3+7}=\frac{5}{10}=\frac{1}{2}$$

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