Assignment 5: Integration Techniques and Applications (80 marks total) Your mark will be given as a percentage. [12 marks] (3 marks) (3 marks) (3 marks) (3 marks) [10 marks] (3 marks} (4 marks} (3 marks} [10 marks] {5 marks} (5marksl [3 marks] [3 marks] 4. 5. Find the following indefinite integrals: a_f(2x2+i,iex+5H)dx b. J (N; i?)2 (11' Suppose that the sales of a companj,r are growing continuousl}P at a rate of STD = 2090.5: where S is in hundreds of dollars per dag.r on dag,P t. a. Find the accumulated sales in dollars for the first 5 days. 13. Find the sales in dollars from the 3"1 dag,r through the 6th day. c. When do the sales exceed $80,001]? Evaluate, giving exact values: 4x2-1 a. L "I; (if): b. gr: max Find the area of region enclosed by the graphs of f[x)=x2xSandf(x)=x+l. Suppose that the population of a countryr can be modelled by NU) = 3090M! where N is in millions and t the number of years since 2000. Find the average value of the population from 2008 to 2012. [12 marks] (4 marks} {4 marks} (4 marks} [10 marks] (6 marks} {4 marks} [10 marks] {5 marks} {5 marks} 6. 7. 8. Find the following indefinite integraLs: a.j'2w3x 2dr 1:. {3:294de c. J'nxfdx a; Suppose that the demand function for a product is given by p = DR) = (I E02 Where x is the number of items and p is the price in dollars per item. Suppose also that the supply function is given by 3(1) = x2 + 12. Find the consumer surplus and the producer surplus. b. Sketch on one graph the supply and demand function, and indicate the consumer surplus and the producer surplus. Determine whether each improper integral is convergent or divergent and find its value if it converges. aurix :. 1 E b.1f39'ixdx