# A granary has the shape of a half cylinder lying on

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Problem 11A granary has the shape of a half cylinder lying on its rectangular side(the cut). The cylinder’s height is 10m, and the radius of the base is 2m. If the granaryis full of barley, with density 600kg/m3, how much work is done in removing all thegrain via an opening at the top of the granary?12
Problem 12Iff(x) is an increasing function on [0,1], rank the following in order fromleast to greatest:f(0)f(1)The left endpoint approximation toR10f(x)dxwithn=5 rectangles.The right endpoint approximation toR10f(x)dxwithn=5 rectangles.The average value offon [0,1].13
Problem 13For each of the following, determine if the improper integral convergesor diverges. If it converges, evaluate the integral.1.R-∞2xe-x2dx2.R-∞12xe-x2dx14
Problem 14A particle starts at the origin at timet=0, and traces out a path given byx(t)=ty(t)=2t2for eacht0.1. Express the lengthl(T) of the path traced out by the particle fromt=0 to a timet=Tas an integral, but do not evaluate it.2. Findl0(T), the speed of the particle at timeT.3. Evaluatel0(2).15