Session 23 Assignments: Chapter 4 Section 4.5

At the end of this lesson, you as a successful student will be able to understand and to use activities

• mean-value theorem
• Fundamental Theorem of Integral Calculus, Part 1
• Fundamental Theorem of Integral Calculus, Part 2

When you finish this lesson, you will complete the Discussion requirement below.

Mean-Value Theorem

At the end of this lesson you will be able to

• state the complete definition of the definite integral
• write the symbol for the definite integral

1. If you have not done it, now study the notes on the MEAN-VALUE THEOREM in the Session 23 notes.
2. In your textbook, review the definition of average value of a function on page 346.
3. In your textbook, review Max-Min Inequality Rule 6 on page 347.
4. In your textbook, study Section 4.5 from page 351 to top of page 352.

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Fundamental Theorem of Integral Calculus, Part 1

At the end of this lesson you will be able to

• use the Fundamental Theorem, Part 1,

1. If you have not done it, now study the notes on the FUNDAMENTAL THEOREM OF INTEGRAL CALCULUS, PART 1 in the Session 23 notes..
2. In your textbook, read Section 4.5 from the bottom of page 353 to Example 3 on page 354.
3. In your textbook, study Section 4.5 from the bottom of page 354 through page 355. Practice Example 3 through 5 on pages 354 through 355 on a separate sheet of paper without looking at the solution in the textbook. Then compare with the textbook solution to insure you understand how the differentiation process operates.
4. On page 361, practice 15(b), 17(b), 19, 21, and 23.

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Fundamental Theorem of Integral Calculus, Part 2

At the end of this lesson you will be able to

• state the Fundamental Theorem of Calculus, Part 2.
• evaluate definite integrals using the Fundamental Theorem of Calculus, Part 2

1. If you have not done it, now study the notes on the FUNDAMENTAL THEOREM OF INTEGRAL CALCULUS, PART 2 in the Session 23 notes..
2. Review the definition of the definite integral in the 4.4 Session 2 Notes and on page 343 of your textbook.
3. In your textbook, study Section 4.5 from the top of page 358 through Example 7 on page 359. Practice Example 7 on page 359 on a separate sheet of paper without looking at the solution in the textbook. Then compare with the textbook solution to insure you understand how to apply the Fundamental Theorem of Integral Calculus.
4. On page 361, practice 1, 3, 5, 7, 9, 11, 13 (Hint: Make two integrals.), 15(a), and 17(a).
5. Practice Supplemental Sheet VI-5, which is found below.

DISCUSSION BOARD

If you are at MyMathLab (CourseCompass), then close this window.  If you are not at MyMathLab, then go to coursecompass.com. 

Click on the (Groups) button at the left, click the underlined group, click on Group Discussion Board, and then click on the "Solutions" discussion forum. Click the "Fund. Th. of Calc." thread and post your solution to one of the problems listed below. Select three (3) problems another student has not yet answered. In your posting, give a complete solution and/or explanation of how obtained your answer.

You are expected to locate errors in any of the other postings. If you are the first to see the error, then you are to help your classmates correct his/her posting. Class participation and helping others is part of the course. Therefore, you who consistently are quick to help your classmates correct errors will receive extra credit for class participation.

Pages 361 Practice any of the even number problems 2 through 22.

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Supplemental Sheet VI-5

Evaluate the following using the Fundamental Theorem of Integral Calculus: