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Calculus 3 DISCUSS WORK ON PRESENT ASSIGNMENT Tuesday, November 25 Volumes over more general regions 97, 101, 102 97, 101 Write up 102 Skip 3.4 Read 4.1 Calendar: Monday, December 1: Tuesday, December 2: Thursday, December 4: Friday, December 5: Wednesday, December 10: 4.1 4.3 Review Review Oral Final Volumes over more general regions We can find volumes over rectangles a < x < b, c < y < d What about volumes over non-rectangular regions? Type I regions z = f(x,y) a < x < b, g(x) < y < h(x) Type II regions z = f(x,y) g(y) < x < h(y), c<y<d dy dx dx dy Many problems are only type I or else only type II, but some problems can be considered either way. Sometimes the math is easier one way. Example: Consider the volume bounded by z = 4 – x – 2y and the coordinate planes. a) Set up integrals for a type I solution b) Set up integrals for a type II solution