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HH_Sec_8_2 - Section 8.2 p 2 Example 3 Find the length of y...

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(9/30/08) Math 10B. Lecture Examples. Section 8.2. Applications to geometry Example 1 The region bounded by the curve y = x - x 4 and the x -axis is rotated about the x -axis. Find the volume of the solid that is generated. Answer: Figures A1a and Figure A1b [Volume] = 1 9 π x 1 y 0 . 5 - 0 . 5 y = x - x 4 Radius at x x r = x - x 4 The region that is rotated The cross section at x Figure A1a Figure A1b Example 2 Find the volume of the solid that is generated when the triangle between the lines y = 1 2 x and y = 2x for 0 x 2 is rotated about the x -axis. Answer: Figures A2a and A2b [Volume] = 10 π. x 2 y 2 4 y = 2 x y = 1 2 x x 1 2 x 2 x The triangle that is rotated The cross section at x Figure A2a Figure A2b Lecture notes to accompany Section 8.2 of Calculus by Hughes-Hallett et al 1
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Math 10B. Lecture Examples. (9/30/08)
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Unformatted text preview: Section 8.2, p. 2 Example 3 Find the length of y = 2 3 x 3 / 2 for ≤ x ≤ 1 . Answer: [Length] = 2 3 (2 3 / 2-1) Example 4 Express the length of y = e x for-1 ≤ x ≤ 1 as a de±nite integral. Answer: [Length] = i 1-1 r 1 + ( e x ) 2 dx Interactive Examples Work the following Interactive Examples on Shenk’s web page, http//www.math.ucsd.edu/˜ashenk/: ‡ Section 7.2: Examples 1–4 Section 7.5: Example 1 ‡ 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_8_2 - Section 8.2 p 2 Example 3 Find the length of y...

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