Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 99278 by Rio Michael last updated on 19/Jun/20

 x         0           2         4          6         8          10   f(x)  2.4       3.6      4.9     6.9     8.0        11.9  Given the curve y = f(x), with corresponding values of  f(x) at certain x values. The curve y = f(x) is rotated  at an angle of 2π about the x−axis. Find   (1) The area of the surface generated using simpson′s rule.  (2) The volume of the surface generated using simpson′s rule.

$$\:{x}\:\:\:\:\:\:\:\:\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\:\:\:\:\:\:\:\:\:\mathrm{4}\:\:\:\:\:\:\:\:\:\:\mathrm{6}\:\:\:\:\:\:\:\:\:\mathrm{8}\:\:\:\:\:\:\:\:\:\:\mathrm{10} \\ $$$$\:{f}\left({x}\right)\:\:\mathrm{2}.\mathrm{4}\:\:\:\:\:\:\:\mathrm{3}.\mathrm{6}\:\:\:\:\:\:\mathrm{4}.\mathrm{9}\:\:\:\:\:\mathrm{6}.\mathrm{9}\:\:\:\:\:\mathrm{8}.\mathrm{0}\:\:\:\:\:\:\:\:\mathrm{11}.\mathrm{9} \\ $$$$\mathrm{Given}\:\mathrm{the}\:\mathrm{curve}\:{y}\:=\:{f}\left({x}\right),\:\mathrm{with}\:\mathrm{corresponding}\:\mathrm{values}\:\mathrm{of} \\ $$$${f}\left({x}\right)\:\mathrm{at}\:\mathrm{certain}\:{x}\:\mathrm{values}.\:\mathrm{The}\:\mathrm{curve}\:{y}\:=\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{rotated} \\ $$$$\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{2}\pi\:\mathrm{about}\:\mathrm{the}\:\mathrm{x}−\mathrm{axis}.\:\mathrm{Find}\: \\ $$$$\left(\mathrm{1}\right)\:\mathrm{The}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{generated}\:\mathrm{using}\:\mathrm{simpson}'\mathrm{s}\:\mathrm{rule}. \\ $$$$\left(\mathrm{2}\right)\:\mathrm{The}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{generated}\:\mathrm{using}\:\mathrm{simpson}'\mathrm{s}\:\mathrm{rule}. \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com