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Unformatted text preview: Co-21B Problem Solving #7T 1) Region R is bounded by x=4y!y2and y=x. SET UP integrals to find the volume of the solids obtained by revolving R about: a) the y axis b) x= -3 c) the x axis e) y= 3 2) Find the length of f(x)=x2/3from x= 1 to x= 8. 3) A thin rod 4 ftlong has a varying density such that the density xfeet from one end is !(x)=x+1lbsfta) Calculate the total mass of the rod. b) Find the rods center of mass. 4) A thin plate covers the region bounded by y=x2andy=x3Assume the density at any point is !(x,y)=2x. a) Find the total mass of the plate b) Find Mx, the moment of the plate about the x-axis. c) Find My, the moment about the y-axis. d) Find x ,y ( ), the plates center of mass. 5) Find the centroid of the region bounded by y=secxand y=on !"/4,"/4[ ]. *Hint: To find secx dx!, multiply top and bottom by secx+tanxand try a usubstitution. 6) Let a> 0, b> 0, and R be the right triangular region with vertices (0, 0), (a, 0) and (a, b)....
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