Unformatted text preview: called &quot;cubic splines&quot;. i) Find a generic formula for the volume generated by spinning the area under a x^3 + b x^2 + c x + d from x=m to x=n, around the x-axis. ii) Adapt your formula (without re-doing any integration) to the polynomial a (x-m)^3 + b (x-m)^2 + c (x-m) + d from x=m to x=n, around the x-axis. Challenge (optional/extra credit) problems: 63 volume of a torus 65 Cavalieri's principle: do it, rather than just reading it. 66 intersecting circular cylinders 70 circular hole in a sphere 72 switching from around x-axis to around a lower horizontal line---------------------------When we get toward the end of Chapter 6, we will work on these Problems Plus problems: (pg 448) #4 tilted cylinder w/water #5a segment of a sphere, c) depth of floating sphere #6 Archimedes principle #7 evaporation, depth of water decreases at a constant rate So, go read them now. Some of them you can even solve now! But they aren't due yet....
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This note was uploaded on 09/08/2011 for the course MATH 121 at Eastern Michigan University.