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Unformatted text preview: MAC2233 Chapter 6 Review 1. Find the indefinite integral R 7 x 3 dx . 2. Find the indefinite integral R 6 √ x 9 x 2 + 5 e x dx . 3. Find the indefinite integral R 2 x 2 7 x 3 dx . 4. Find the indefinite integral R ( x + 2) 3 dx . 5. Given f ( x ) = e x 2 x and f (0) = 2, find f ( x ). 6. Find the indefinite integral R 3 x 2 +2 ( x 3 +2 x ) 2 dx . 7. Find the indefinite integral R e x (1 + e x ) dx . 8. Find the indefinite integral R 5 x (ln x ) 4 dx . 9. The population of a certain city is projected to grow at the rate of r ( t ) = 400 1 + 2 t 24 + t 2 (0 ≤ t ≤ 5) people/year, t years from now. The current population is 60,000. What will be the population 5 years from now? 10. Approximate the area under the curve f ( x ) = 4 x 2 , x ∈ [0 , 2] , using four rectangles of equal width and the midpoint of each resulting interval as the sample point. Use a definite integral to find the exact area. 11. Approximate the area under the curve f ( x ) = 2 x, x ∈ [0 , 3] using six rectangles and the left endpoint of each interval as the sample point. Use a definite integral to find the exact area. 12. Find the area of the region under the graph of f ( x ) = 2 x + x 6 on the interval [0 , 2]. 1 13. Evaluate the definite integral R 9 1 x 1 √ x dx . 14. The management of Ditton Industries has determined that the daily marginal revenue function associated with selling x units of their deluxe toaster ovens is given by R ( x ) = . 1 x + 40 where R ( x ) is measured in dollars/unit. Find the daily total revenue realized from the sale of 200 units of the toaster oven. Find the additional revenue re alized when the production (and sales) level is increase from 200 to 300 units. 15. Evaluate the definite integral R 2 x √ x 2 +5 dx . 16. Evaluate the definite integral R 4 1 e √ x √ x dx . 17. Find the average value of f ( x ) = 4 x 2 on [ 2 , 3]. 18. Find the area of the region enclosed by f ( x ) = 9 x 2 , g ( x ) = x +3, x = 1, and x = 5. 19. Find the area between the curve y = ( x 1)( x + 2) and the xaxis for x ∈ [0 , 3]. 20. Because of the increasingly important role played by coal as a viable alternative energy source, the production of coal has been growing at the rate of 3 . 5 e . 05 t billion metric tons/year, t years from 1980 (which corresponds to t = 0)....
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 Spring '08
 Smith
 Calculus, dx

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