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Unformatted text preview: n . Hence, the limit of Riemann sums is the denite integral : Let S be the solid obtained by rotating about the y-axis the region under the curve y = f ( x ) from a to b (where 0 a < b ). The volume of this solid S is: V = lim n n X i =1 (2 x * i )[ f ( x * i )] 4 x = Z b a (2 x )[ f ( x )] dx Notice : To remember the formula to compute the volume of a cylindrical shell, think of a typical shell, cut and attened, with radius x , circumference 2 x , height f ( x ), and thickness dx (or 4 x ). Example 1 of Section 6.3 (textbook): Example 2 of Section 6.3 (textbook): Example 3 of Section 6.3 (textbook): Example 4 of Section 6.3 (textbook): 1...
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This note was uploaded on 05/23/2011 for the course MAC 2311 taught by Professor Noohi during the Fall '08 term at FSU.
- Fall '08