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Unformatted text preview: x ) dx Your signature: (5) Use geometry to ﬁnd the exact value of the following integrals. (a) Z 4 1  x2  dx (b) Z 5 √ 25x 2 dx Your signature: (6) Use geometry to ﬁnd the exact value of Z 66  x1  dx + Z 66 √ 36x 2 dx Your signature: (7) Given f ( x ) = √ 49x 2 ﬁnd the average value of f ( x ) over the interval 0 ≤ x ≤ 7. Your signature: (8) For the function f below, consider the average value of f over the following intervals: I. ≤ x ≤ 1 II. ≤ x ≤ 2 II. 0 ≤ x ≤ 5 IV.2 ≤ x ≤ 2 (a) For which interval is the average value of f least? (b) For which interval is the average value of f greatest? (c) For which pair of intervals are the average values equal?...
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 Fall '09
 HarvanshManocha
 Calculus, #, Order theory, Polytechnic Institute of NYU MA

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