Unformatted text preview: the Riemann sum ): V ≈ ∑ n i =1 A ( x * i ) 4 x . This approximation appears to become better and better as n → ∞ . (Think of the slices as becoming thinner and thinner.) Therefore, we deﬁne the volume as the limit of these sums as n → ∞ . Also, this limit of Riemann sums is the deﬁnite integral : Let S be a solid that lies between x = a and x = b . If the crosssectional area of S in the plane P x , through x and perpendicular to the xaxis, is A ( x ), where A is a continuous function, then the volume of S is: V = lim n →∞ Σ n i =1 A ( x * i ) 4 x = Z b a A ( x ) dx Example 1 of Section 6.2 (textbook): Example 2 of Section 6.2 (textbook): Example 3 of Section 6.2 (textbook): Example 4 of Section 6.2 (textbook): Example 5 of Section 6.2 (textbook): Example 6 of Section 6.2 (textbook): Example 7 of Section 6.2 (textbook): 1...
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 Fall '08
 Noohi
 Calculus, crosssectional area, Ms. Hoa Nguyen, ith slab Si, plane Px

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