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# test 4 - Name Math 160 Test#4 Integration For the problems...

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Name: __________ Math 160 Test #4: Integration For the problems marked Calculator-free, no calculators may be used. You must show all work for these problems so that I can see, step by step, how it is done. Part I: Anti-derivatives Find the anti-derivative or integrate, as indicated. No calculators permitted for this part. 1. f ' x = x 2 6 x x 2. r ' s = s 2 2 s 3. du dv = v 1 v 2 4. x 6 x dx 5. x x 6 dx 6. x 2 x 3 1 dx 7. Find the equation of the line with slope y' = e 2 x 1 that passes through (0,5). Part II: Fundamental Theorem of Calculus 8. Estimate the area under the curve y = 9 x 2 from x = 0 to x = 3 A. Using L 3 B. Using R 3 C. Using M 3 D. What is the maximum error for this area if we partition it into three intervals? E. How many intervals would we need to calculate the area to the nearest tenth?

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Part III: Area You may use a calculator as necessary, but I need to see you set up the integral. Showing all work up to that point (especially sketching graphs) would be helpful, too.
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