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Review 5 - MAC2233 Chapter 6 Review 1 Find the indefinite...

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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 x-axis 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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Review 5 - MAC2233 Chapter 6 Review 1 Find the indefinite...

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