Ch 19: Approximation of Definite Integrals

About This Chapter

Practice making approximations of areas with curved-line borders in this chapter on evaluating definite integrals. See how well you're doing by taking the chapter test.

Approximation of Definite Integrals - Chapter Summary and Learning Objectives

This chapter returns to Riemann sums and how they might be used in a variety of ways to make approximations. Our expert instructors will walk you through the process of making approximations using increasingly accurate shapes and rectangle widths before discussing the average value theorem. After watching the videos take the assessments to get an idea of which areas you may want to review. The lessons in this chapter include discussions of:

  • The Trapezoid Rule
  • Riemann sums, including left, right, and middle Riemann sums
  • The Average Value Theorem

Video Objective
What is the Trapezoid Rule Learn to get more accurate in approximations by using trapezoids, which can closer approach the shape of a curved line, rather than rectangles.
How to Use Riemann Sums to Calculate Integrals Math-by-lawnmower is the topic of this video discussing approximations using a series of rectangles of equal width.
How to Identify and Draw Left, Right and Middle Riemann Sums Sometimes you want your rectangles to be entirely within the area, others times you want to overestimate: learn how to determine at which point the function will intersect with the top of your rectangles.
Average Value Theorem In this video our instructors explain how to find the average value of a function and how to use that to determine an area defined by a curved line.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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