8. 10. [10 marks] Evaluate the following integrals. Show all work. Leave your answer in (a) as a simplied exact number, not as a decimal. a) f \"1;, a [{1an l [5 marks] In thousands of dollars per widget, a manufacturer estimates that its marginal cost to produce 1: widgets is given by f {I} = 222-1-1, while its marginal revenue is given by 9(3) = :i:2 + 12:: +2. Determine the total prot if 10 widgets are sold. [4 marks] A traic engineering rm estimates that the average (mean) wait time for a vehicle to enter a proposed roundabout at rush hour is 14.0 seconds with a standard deviation of 1.6 seconds. Assuming a standard normal distribution, what is the probability that a vehicle's wait time to enter a roundabout is between 10.0 and 16.4 seconds? Show all work and then use the slider tool found within the lecture on The Standard Normal Distribution to determine the probability