HH_Sec_7_7 - Answer[Average value = 3 4 • The area of...

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(9/30/08) Math 10B. Lecture Examples. Section 7.7. Improper integrals Example 1 Evaluate i 3 1 x 3 dx . Answer: i 3 1 x 3 dx = 1 18 Example 2 Find the area of the region between y = 1 / x and the x -axis for x 1 . Answer: Figure A1 [Area] = x 1 2 3 4 y 1 y = 1 x Figure A1 Example 3 Is i 0 cos x dx de±ned? Answer: i 0 cos x dx is not defned. Example 4 Evaluate i 9 0 1 x dx . Answer: i 9 0 1 x dx = 6 Lecture notes to accompany Section 7.7 o± Calculus by Hughes-Hallett et al 1
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Math 10B. Lecture Examples. (9/30/08) Section 7.7, p. 2 Example 5 Find the average value of y = x - 1 / 3 for 0 x 8 and give a geometric interpretation of the result.
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Unformatted text preview: Answer: [Average value] = 3 4 • The area of region A is equal to the area of region B in Figure A5. x 4 8 y y = x-1 / 3 3 4 A B Figure A5 Interactive Examples Work the following Interactive Examples on Shenk’s web page, http//www.math.ucsd.edu/˜ashenk/: ‡ Section 8.6: Examples 1–5 ‡ The chapter and section numbers on Shenk’s web site refer to his calculus manuscript and not to the chapters and sections of the textbook for the course....
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HH_Sec_7_7 - Answer[Average value = 3 4 • The area of...

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