5: Integration Techniques and Applications (80 marks total) Your mark will be given as a percentage. [12 marks] 1. Find the following indefinite integrals: (3 marks) a. (3 marks) b. (3 marks) c. (3 marks) d. [10 marks] 2. 3 5 Suppose that the sales of a company are growing continuously at a rate of 20 . where is in hundreds of dollars per day on day . (3 marks) a. Find the accumulated sales in dollars for the first 5 days. (4 marks) b. Find the sales in dollars from the 3rd day through the 6th day. (3 marks) c. When do the sales exceed $80,000? [10 marks] 3. Evaluate, giving exact values: (5 marks) a. (5marks) b. 12 [8 marks] 4. Find the area of region enclosed by the graphs of 6. and [8 marks] 5. Suppose that the population of a country can be modelled by 30 . where is in millions and the number of years since 2000. Find the average value of the population from 2008 to 2012. [12 marks] 6. Find the following indefinite integrals: (4 marks) a. (4 marks) b. (4 marks) c. [10 marks] 2 3 2 ln 7. (6 marks) a. Suppose that the demand function for a product is given by 6 where is the number of items and is the price in dollars per item. Suppose also that the supply function is given by 12. Find the consumer surplus and the producer surplus. (4 marks) b. Sketch on one graph the supply and demand function, and indicate the consumer surplus and the producer surplus. [10 marks] 8. Determine whether each improper integral is convergent or divergent, and find its value if it converges. (5 marks) a. (5 marks) b. 3