Unformatted text preview: n → ∞ . Hence, the limit of Riemann sums is the deﬁnite integral : Let S be the solid obtained by rotating about the yaxis 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 πx * i )[ f ( x * i )] 4 x = Z b a (2 πx )[ f ( x )] dx Notice : To remember the formula to compute the volume of a cylindrical shell, think of a typical shell, cut and ﬂattened, with radius x , circumference 2 πx , 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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 Fall '08
 Noohi
 Calculus, cylindrical shell, Ms. Hoa Nguyen, average radius x∗

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