Use-Trapezoidal-rule-with-ordinate-1-1-5-2-2-5-3-to-compute-1-3-x-1-x-dx-Mastermind-

Question Number 170413 by Mastermind last updated on 23/May/22

$${Use}\:{Trapezoidal}\:{rule}\:{with}\:{ordinate} \\ $$$$\mathrm{1},\:\mathrm{1}.\mathrm{5},\:\mathrm{2},\:\mathrm{2}.\mathrm{5},\:\mathrm{3}\:{to}\:{compute} \\ $$$$\int_{\mathrm{1}} ^{\mathrm{3}} \frac{\sqrt{{x}+\mathrm{1}}}{{x}}{dx}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Answered by MikeH last updated on 23/May/22

$$\begin{array}{|c|c|}{{x}}&\hline{\mathrm{1}}&\hline{\mathrm{1}.\mathrm{5}}&\hline{\mathrm{2}}&\hline{\mathrm{2}.\mathrm{5}}&\hline{\mathrm{3}}\\{{y}=\frac{\sqrt{{x}+\mathrm{1}}}{{x}}}&\hline{\mathrm{1}.\mathrm{41}}&\hline{\mathrm{1}.\mathrm{05}}&\hline{\mathrm{0}.\mathrm{866}}&\hline{\mathrm{0}.\mathrm{748}}&\hline{\mathrm{0}.\mathrm{667}}\\\hline\end{array} \\ $$$$\int_{\mathrm{1}} ^{\mathrm{3}} \frac{\sqrt{{x}+\mathrm{1}}}{{x}}{dx}\:\approx\:\frac{\mathrm{0}.\mathrm{5}}{\mathrm{2}}\left[\mathrm{0}.\mathrm{667}\:+\mathrm{1}.\mathrm{42}\:+\mathrm{2}\left(\mathrm{1}.\mathrm{05}+\mathrm{0}.\mathrm{866}+\mathrm{0}.\mathrm{748}\right)\right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{1}.\mathrm{85} \\ $$

Commented by Mastermind last updated on 24/May/22

$$ \\ $$$${Thanks} \\ $$

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