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Unformatted text preview: write up his or her own solution. 1. Let R be the region bounded by the curves y = e x , y = e 2 x , and y = e 4 . (a) Sketch the region and ﬁnd its area. (b) Express the volume of the region obtained by rotating R about the y axis as a deﬁnite integral (do not evaluate). 2. Diﬀerentiate f ( x ) = (ln x ) cos x . 3. Evaluate the integrals below. (a) Z ln2 e 3 x e 3 x + 1 dx . (b) Z 3 2 dx 9 + 4 x 2 (c) Z 1 2 ln3 e x √ 4-e 2 x dx...
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This note was uploaded on 11/30/2010 for the course M 408c taught by Professor Mcadam during the Spring '06 term at University of Texas at Austin.
- Spring '06