Question

х 12 11. The following table shows data of measurement taking of a region of mass, where L(x) is the length of the region at position x. 0 3 6 9 15 18 L(x) 9.8 9.1 8.5 8.0 7.7 7.5 7.4 a. Use Simpson's rule to approximate the area described by this region: SoL(x)dx 18 b. Using Simpson's rule and the table above, find the approximate center of mass of the region. (10 points)

Answer 1

a) Here h = sparing length = 3 ei yLou 2:16) 9x 0 0 9.8 Y + | (%+4) 3 BI 3 9.1 273 Simpson's į rule 31,200 461197, +45) 42 (4+%)] ${(1,347.1)44,(311 30 * 7.5)- 2425477 (17.2 + 4x 24,16 +27 16-2) 2 6 8.5 51.0 3 9 8.0 7200 148 12. 7.7 1924 Hence area 5 15 7.5 Rrele 112.5 the regd. apprevinato described by this region using Simpson's 18 L (x) dx ܘܢ 18 7.4 1332 unit Creed.) 148 Square By 6). centre of ssoue s x. 20 de 1200) do Simpson's rule so x2(x) dx Í [fro Low +2210913 +4{X/L(x) + 2, L03) +854(15)} +2{k92 (83) +74L (24)}} ** | (0+133.2) +4(37.34 112-5) +2 ( 510+92-4) 1267.2., 148 72.0+ ?. 8.562 (rounded up to 3.decimal places <Regd.) 1) 133.2 + 4x21118 +2 r 12672 143.4

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