After completing this section, students should be able to do the following.Apply the procedure of “Slice, Approximate, Integrate” to derive a formula for the area bounded by given curves.Understand the difference between net and total area.Find the area bounded by several curves.Set up an integral or sum of integrals with respect to xx that gives the area bounded by several curves.Set up an integral or sum of integrals with respect to yy that gives the area bounded by several curves.Decide whether to integrate with respect to xx or yy.
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.