Question Number 9623 by tawakalitu last updated on 21/Dec/16
$$\mathrm{Evaluate}\::\:\int_{\mathrm{4}} ^{\mathrm{5}.\mathrm{2}} \:\mathrm{ln}\left(\mathrm{x}\right)\:\mathrm{dx}\:\: \\ $$$$\mathrm{using}\:\mathrm{trapezoidal}\:\mathrm{rule}.\:\mathrm{take}\:\mathrm{h}\:=\:\mathrm{0}.\mathrm{2} \\ $$
Commented by sandy_suhendra last updated on 21/Dec/16
Answered by sandy_suhendra last updated on 21/Dec/16
![∫_4 ^( 5.2) ln x dx ≈((Δx)/2)[f(4)+2f(4.2)+2f(4.4)+...+2f(5)+f(5.2)] ≈((0.2)/2)[ln4+2ln4.2+...+2ln5+ln5.2] ≈0.1 ln [4×4.2^2 ×4.4^2 ×4.6^2 ×4.8^2 ×5^2 ×5.2] ≈0.1×18.24 (I use calculator) ≈1.824](https://www.tinkutara.com/question/Q9625.png)
$$\int_{\mathrm{4}} ^{\:\:\mathrm{5}.\mathrm{2}} \:\mathrm{ln}\:\mathrm{x}\:\mathrm{dx}\: \\ $$$$\approx\frac{\Delta\mathrm{x}}{\mathrm{2}}\left[\mathrm{f}\left(\mathrm{4}\right)+\mathrm{2f}\left(\mathrm{4}.\mathrm{2}\right)+\mathrm{2f}\left(\mathrm{4}.\mathrm{4}\right)+…+\mathrm{2f}\left(\mathrm{5}\right)+\mathrm{f}\left(\mathrm{5}.\mathrm{2}\right)\right] \\ $$$$\approx\frac{\mathrm{0}.\mathrm{2}}{\mathrm{2}}\left[\mathrm{ln4}+\mathrm{2ln4}.\mathrm{2}+…+\mathrm{2ln5}+\mathrm{ln5}.\mathrm{2}\right] \\ $$$$\approx\mathrm{0}.\mathrm{1}\:\mathrm{ln}\:\left[\mathrm{4}×\mathrm{4}.\mathrm{2}^{\mathrm{2}} ×\mathrm{4}.\mathrm{4}^{\mathrm{2}} ×\mathrm{4}.\mathrm{6}^{\mathrm{2}} ×\mathrm{4}.\mathrm{8}^{\mathrm{2}} ×\mathrm{5}^{\mathrm{2}} ×\mathrm{5}.\mathrm{2}\right] \\ $$$$\approx\mathrm{0}.\mathrm{1}×\mathrm{18}.\mathrm{24}\:\left(\mathrm{I}\:\mathrm{use}\:\mathrm{calculator}\right) \\ $$$$\approx\mathrm{1}.\mathrm{824} \\ $$
Commented by tawakalitu last updated on 21/Dec/16
$$\mathrm{i}\:\mathrm{really}\:\mathrm{appreciate}\:\mathrm{your}\:\mathrm{effort}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless} \\ $$$$\mathrm{you}. \\ $$