Question

. . Show all of your work. Label the axes and scale on your graph. The sketch should include at least three to five points including the points of intersection and at least one point in between. . The integration techniques used should be clear and easy to follow step by step with all techniques shown in detail, including the substitution method. . . All steps must be shown in your own writing to receive any credit. Circle or box your final answers. Draw a line separating each problem. Find the center of mass of the lamina that occupies the region R with the given density function. R = {y = 0,y 4 =-X = х 1,x = 4); 8(x,y) kx?

Answer 1

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where } = { ugandy ,S=kn2 R. R 4D y=4 yzo A B strip 2-1 14 4 41x 4 410 4 Center of mass=ln, jl ñ= slagandy Ileandy I Sandy where R is the region bounded by y=0, y = 4 4 221 4 4 first owe draw the region Now find Rt q intersections N=1 = y = 4 = 4D = (1,4) X=1, y = 0 ,A=(1,0) B = 4,920, B=(4,0) 2:42 9 = 4 = 1 (=(4,1) First we calculate Denomenator of n ý limit consider vertical ship led to x-axis where y=0 to y 4 4 4 of rotate this strip along x-axis from n=1 to n = 4 Ileandy = f (kn dy dn = k/n?{y] an= klare holdin con cn = k leczy 1 * = K[2643–2007) = 3015 Slong andy = f (x) ay an = klopty to cane = klo 14 - 03 din k Saxion 24k (1 28 14 = 4k (432 133 ) = 846 I lysandy = f ( t r dy dn = klo 14 d. Klar for offen = k1*80m = {(3) (>11*= 8k (4-1) = 24k x=846 55= 15 9 = 26 4 4 center of mass = = (1,5) =(4, 5) R 0 4 - - y= 4 5 3ok