Chapter 5: Integrals

Class Notes

• 5.1 Areas and Distances (pdf)
• 5.2 The Definite Integral (pdf)
• 5.3 Evaluating Definite Integrals (pdf)
• 5.4 The Fundamental Theorem of Calculus (pdf)
• 5.5 The Substitution Rule (pdf)
• 5.6 Integration by Parts (pdf)
• 5.7 Additional Techniques of Integration (pdf)
• 5.8 Integration Using Tables and Computer Algebra Systems (pdf)
• 5.9 Approximate Integration (pdf)
• 5.10 Improper Integrals (pdf)

Homework

• 5.1 -- 1, 2, 3, 7, 11, 12, 13, 15, 17, 18
• 5.2 -- 1, 6, 11, 16, 20, 23, 30, 32, 35, 40, 41, 42, 48, 49
• 5.3 -- 1, 2, 4, 6, 12, 15, 18, 23, 28, 30, 31, 40, 49, 54, 57, 60
• 5.4 -- 3, 4, 9, 12, 15, 18, 19, 22, 24, 27
• 5.5 -- 4, 5, 14, 16, 18, 22, 28, 35, 45, 48, 51, 52, 61, 63
• 5.6 -- 2, 3, 9, 14, 19, 21, 25, 37, 41, 43
• 5.7 -- 1, 2, 5, 6, 7, 9, 10, 14, 16, 18, 20, 21, 27, 32
• 5.8 -- 2, 7, 10, 16, 18, 20, 21, 32, 33
• 5.9 -- 1, 7, 13, 16, 24, 25 (use midpoint rule), 32, 33, 35
• 5.10 -- 1, 3, 6, 14, 17, 23, 29, 40, 43, 44, 46, 47, 53, 57, 62

Mathematica Notebooks

The following Mathematica notebooks are available in two formats. Download the Mathematica notebooks (nb) to your machine and use Mathematica to interpret their contents, or click on the web page link (html) to see a static image of the evaluated notebook.

• 5.1 Areas and Distances nb html
• 5.2 The Definite Integral nb html
• 5.3 Evaluating Definite Integrals nb html
• 5.4 The Fundamental Theorem of Calculus nb html
• 5.5 The Substitution Rule nb html
• 5.6 Integration by Parts nb html
• 5.7 Additional Techniques of Integration nb html
• 5.8 Integration Using Tables and Computer Algebra Systems nb html
• 5.9 Approximate Integration nb html
• 5.10 Improper Integrals nb html

Lab Exercises (Optional!)

These lab exercises are optional, but working on them should be helpful!

Using some of the solved exercises in our Mathematica notebooks for this chapter as a guide, try to develop complete Mathematica notebook solutions to some of the following homework exercises. We may work on a few of these projects in class, as time allows.

• 5.1.9 Riemann sums for f(x) = sqrt(x) over [1,4] with n = 10, 30, 50 using lefthand and righthand endpoints
• 5.2.11 and 5.2.13 Riemann sums for g(x) = sqrt(1 + x^2) over [1,2] for n = 10, 20, 30 using midpoint approximations