Lesson 3: 11.3 The Integral Test and Estimates of Sums
Duration of Days: 3
Lesson Objective
Students will be able to apply the Integral Test to determine whether a series converges or diverges, and will be able to estimate the sum of a convergent series.
- How is the integral of a function related to the corresponding series?
- If an integral converges, does the related series also converge?
- How can we estimate the sum of a convergent series using the integral of the corresponding function?
- Integral Test
- Remainder estimate for the Integral Test
(determine whether a series converges and estimating the sum if it does)
- To determine whether an infinite series converges or diverges using the associated integral, and estimating the infinite sum when it converges.
- DOK Levels 1-4
- calculating total future value of annuities and investments
- calculating materials needed for construction
- radioactive decay and population growth
It is sometimes difficult for students to find the function that is related to the series in order to do the integral.
Homogeneous grouping and whole class discussion
section assessment
problems assigned from book