1) A plate is bounded by the curves y = 0, y = x^2 + 1, x = -1 and x = +1. It has density d(x,y) = x^2. Find its center of mass (x bar, y bar)
2) Find the length of the path c'. x = 1, y = t, z = t^2/2, t is greater than or equal to 0 and less than or equal to 1.
Center of mass and length of path are determined. The solution is detailed and well presented.