MATH138 Lecture 4: Week 4 (lec 9-11) Lecture Notes

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Recall volumes of revolution using disks and washers. a b. For this we must invert the function to get and y d c x. Find the volume of revolution of the curve. About the x-axis then about the y-axis where. To begin, we must invert this equation to find . If we have a curve that is piecewise constant, To compute the volume of revolution about the y-axis we use our formula. If we have subintervals, each of which has a constant height, we find the total volume of revolution by summing up the volume of each shell. If our interval is centred at and has width then. If we rotate our curve about the x-axis. Disks (washer) f(x) a b (about x) g(y) d c (about y) Shells f(x) d g(y) a b (about y) c (about x) Find the volume of rotating the curve in the domain about the -axis using shells. y=1.