Session 25 Assignments: Chapter 4 Sections 4.4 and 4.6

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

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

Geometric Interpretation of Definite Integral

At the end of this lesson you will be able to

  1. If you have not done it, now study the notes on the GEOMETRIC INTERPRETATION OF DEFINITE INTEGRAL in the Session 25 notes.
  2. In Section 4.4 of your textbook, study from the middle of page 342 through the middle of page 343.
  3. In Section 4.4 of your textbook, study from the top of page 345 through the definition of the area under a curve.

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Evaluating Areas

At the end of this lesson you will be able to

  1. If you have not done it, now study the notes on the EVALUATING AREAS in the Session 25 notes.
  2. In your textbook, study Section 4.6 from page 367 (Area between curves) through the top of page 371. Practice Examples 4 and 5 on a separate sheet of paper without looking at the solution in the textbook. Then compare your solution with the textbook solution to insure you understand. Do pay particular attention to the rectangles the authors placed in Figure 4.22 and Figure 4.23.
  3. On page 372 in your textbook, practice 19 (use the double angle identity for (cos x)^2 to find an exact differential), 21, 29 (use symmetry), 31, 33, 35, 39, and 41.
  4. Practice the following:

a. Find the area between the curves y = cos (x) and y = - sin (x) from x = 0 to x = pi/2. (Ans. Area between the curves is 2.)

b. Find the area enclosed by the line y = 2x and the curve y = x^3 + 2x^2 - 3x + 1. (Make two integrals and use your graphing calculator as described in the notes for this section.) (Ans. Area is approximately 26.15341.)

c. Find the area above the line y = 2x and below the curve y = e^(-x^2) in the first quadrant. (Use your graphing calculator.) (Ans. Area is approximately 0.22016.)

d. Find the area in the first quadrant bounded by the curve x = 12 (y^2 - y^3) and the y-axis. (Use y as the independent variable, although you could use x.) (Ans. Area between the curves is 1.)

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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 "Area" thread and post your solution to two of the problems listed below. Select 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.

On page 372 in your textbook, practice: 22, 26, 28, 30, 32, 36 or 40.

Or practice the following:

a. Find the area bounded by the curve x = y^2 and line x = 4.

b. Find the area bounded by the curve x = 3y - y^2 and line x + y = 3.

c. Find the area in the first quadrant bounded by the curve x = y^3 and x = y^2.

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