After completing this section, students should be able to do the following.Understand what a solid of revolution is and the two ways to generate one.Use the procedure of “Slice, Approximate, Integrate” to derive the washer method formula.Use the procedure of “Slice, Approximate, Integrate” to derive the shell method formula.Set up an integral or sum of integrals using the washer method.Set up an integral or sum of integrals using the shell method.Compute volumes using the washer method.Compute volumes using the shell method.Determine whether to use washer or shell method given the variable of integration.Determine the variable of integration given the method.Determine if washer method or shell method is more convenient to set up a volume.
Ohio Transfer Module Mathematics, Statistics, and Logic (TMM) Standards
Core TMM006 Outcome: Core skill demonstrated by students who successfully complete a Calculus II Course
Standard: Use antiderivatives to evaluate definite integrals and apply definite integrals in a variety of applications to model physical, biological or economic situations. Whatever applications (e.g. determining area, volume of solids of revolution, arc length, area of surfaces of revolution, centroids, work, and fluid forces) are chosen, the emphasis should be on setting up an approximating Riemann sum and representing its limit as a definite integral.