New Week 3 – 7.3 Definite Integrals

Step 1: Week 3 kickoff meeting – Monday 10:10 am

• You can see the recording of Monday’s meeting from the link in Canvas
• Agenda: Discuss new Week 3 instructions with different structure (built to help you start the HW more quickly), discuss the definition of the “definite integral”, give an overview of the main theorems in the section.

Step 2: Get started on the WebAssign homework ASAP

• Log into WebAssign from Canvas and start the Section 7.3 homework
• Be sure to use the e-book when you need help and to look at relevant definitions, theorems, and examples
• Problems 1-2 ask you to calculate definite integral values using geometry and areas of things you know about, like triangles and circles.
  • You’ll also have to understand how area under the x-axis is counted negatively; see Theorem 7.10 and the figure below it in the e-book.
  • This Common Geometric Area video from ProfRobBob goes through worked examples of these types of problems.
• Problems 3-5 ask you to calculate definite integral values using other known definite integral values, and properties of definite integrals.
  • The properties are listed in Theorems 7.11 and 7.12; see also Example 4.
  • This Properties of Definite Integrals video by Cassie Williams can help you understand why these properties are true (don’t worry about the formal proof at the end).
• Problems 6-7 ask you to set up definite integrals as limits of Riemann sums, and then compute those sums for large values of n, and then as n “goes to infinity”.
  • See Definition 7.9 in the e-book, and Examples 1 and 2.
  • The Section 7.3 Calc Clips video linked in the WebAssign Resources is also an example of this type of problem.
  • Since this is a difficult concept, it may be worth watching another! Basically the same content but with a more excitable person and better production values is in this Trefor Bazett video on the Definite Integral from a limit of Riemann sums.
  • For even more practice with definite integrals as limits of Riemann sums, watch the three Khan Academy videos starting at this link.
• Problems 8-9 ask you to calculate definite integral values using the formulas for certain simple definite integrals.
  • See Theorem 7.13 and Example 3
  • You may have to use algebra or definite integral properties to split up the definite integrals to make them match the ones in Theorem 7.13 so you can apply those formulas.

Step 3: Take a break

• Sit outside in the sun alone and close your eyes and listen to the wind pass through the new leaves on the trees. Deep breath. This time is just for you and you don’t need to do anything but sit in the sun for now.

Step 4: Get help if you need it… until you’ve finished and mastered the homework

• Attend the Zoom drop-in 4-6pm Thursday (link in Canvas)
  • Or, if you can’t attend, watch the recording (link to be added in Canvas later)
  • Agenda: Discuss wekly updates, get math help, ask Dr. Taalman anything
• If you need help now or at any point: For math questions, use Canvas Chat or Discussion, or contact the SMLC. For other questions text Dr. Taalman directly.

Step 5: Take the Mastery Quiz for Section 7.3

• When you’re ready, take the 7.3 Mastery Quiz in Canvas (and retake if needed)
• I recommend you take your first quiz attempt by Friday or Saturday
• Click here to read details about quizzes - read BEFORE ATTEMPTING any quiz
  • The rules for Mastery Quizzes are now different. For each section in Chapter 7 you will have exactly two opportunities to take the quiz for that section, and both of those attempts need to be completed in Canvas by the end-of-week deadline of 11:59pm on Sunday.
  • (For retakes of previous quizzes, I am working on a solution that I will announce in about a week. Most likely you will get a fixed amount of retakes for previous quizzes. The final exam structure will be announced later, but optimally will also consist of Mastery Quiz retakes.)
  • During each attempt you will have 15 minutes to answer three questions. The questions will appear one at a time and you will not be able to go back to previous questions. You will be able to see your quiz responses only one time, at the very end of the quiz.
  • As always, the quiz questions are randomized from a large bank of problems that are based on the homework assignments. This means that your second-attempt quiz will likely have completely different problems than your first-attempt quiz, which means that the best way to prepare for your retake is to study the homework assignments.
  • I strongly recommend that you wait at least 24 hours after your first quiz attempt before attempting your one and only retake for that section; therefore you should try to take the quiz the first time by Saturday afternoon so that you have time to take the retake on Sunday before the 11:59 pm deadline.
  • You are on your JMU honor to complete each quiz without any outside assistance; no calculators, computers, phones, or any other technology or help from other people.
  • Because other students will take quizzes at different times, you are also on your honor to not share any information about any quiz or its contents with anyone else. I will take honor violations very seriously; your respect for the JMU honor code will allow us to complete this course online. Thank you for making this possible.

You must finish the WebAssign homework and both quiz attempts before 11:59 pm on Sunday — but having said that, these are not normal times; please just text me if you need an extension due to personal, economic, or family situations.

When you’re done with everything, please fill out this End-of-week-3 Survey.

Have a good week and please let me know if you need anything at all. And stay home 🙂