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 | ||
$$\int_{\mathrm{4}} ^{\:\:\mathrm{5}.\mathrm{2}} \:\mathrm{ln}\:\mathrm{x}\:\mathrm{dx}\: \\ $$$$\approx\frac{\Delta\mathrm{x}}{\mathrm{2}}\left[\mathrm{f}\left(\mathrm{4}\right)+\mathrm{2f}\left(\mathrm{4}.\mathrm{2}\right)+\mathrm{2f}\left(\mathrm{4}.\mathrm{4}\right)+...+\mathrm{2f}\left(\mathrm{5}\right)+\mathrm{f}\left(\mathrm{5}.\mathrm{2}\right)\right] \\ $$$$\approx\frac{\mathrm{0}.\mathrm{2}}{\mathrm{2}}\left[\mathrm{ln4}+\mathrm{2ln4}.\mathrm{2}+...+\mathrm{2ln5}+\mathrm{ln5}.\mathrm{2}\right] \\ $$$$\approx\mathrm{0}.\mathrm{1}\:\mathrm{ln}\:\left[\mathrm{4}×\mathrm{4}.\mathrm{2}^{\mathrm{2}} ×\mathrm{4}.\mathrm{4}^{\mathrm{2}} ×\mathrm{4}.\mathrm{6}^{\mathrm{2}} ×\mathrm{4}.\mathrm{8}^{\mathrm{2}} ×\mathrm{5}^{\mathrm{2}} ×\mathrm{5}.\mathrm{2}\right] \\ $$$$\approx\mathrm{0}.\mathrm{1}×\mathrm{18}.\mathrm{24}\:\left(\mathrm{I}\:\mathrm{use}\:\mathrm{calculator}\right) \\ $$$$\approx\mathrm{1}.\mathrm{824} \\ $$ | ||
Commented by tawakalitu last updated on 21/Dec/16 | ||
$$\mathrm{i}\:\mathrm{really}\:\mathrm{appreciate}\:\mathrm{your}\:\mathrm{effort}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless} \\ $$$$\mathrm{you}. \\ $$ | ||