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Unformatted text preview: Exam 3 Review 18.01 Fall 2006 Lecture 25: Exam 3 Review Integration 1. Evaluate definite integrals. Substitution, first fundamental theorem of calculus (FTC 1), (and hints?) 2. FTC 2: d x f ( t ) dt = f ( t ) dx a x If F ( x ) = f ( t ) dt , find the graph of F , estimate F , and change variables. a 3. Riemann sums; trapezoidal and Simpsons rules. 4. Areas, volumes. 5. Other cumulative sums: average value, probability, work, etc. There are two types of volume problems: 1. solids of revolution 2. other (do by slices) In these problems, there will be something you can draw in 2D, to be able to see whats going on in that one plane. In solid of revolution problems, the solid is formed by revolution around the x-axis or the y-axis. You will have to decide how to chop up the solid: into shells or disks. Put another way, you must decide whether to integrate with dx or dy . After making that choice, the rest of the procedure is systematically determined. For example, consider a shape rotated...
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