Show all steps in the solutions to the following questions. Insufficient justification will result in a loss of marks. 1. [6 marks] Evaluate each of the following definite integrals. [Leave your answer in exact form; i.e., no decimals.] (a) j (ln x) dr T 5x (b) 1 de dx 2. [6 marks] The revenue of lift ticket sales at ski hills is related to the amount of snowfall in a season. Suppose that the rate of change of revenue based on the total snowfall accumulation, in dollars/cm, is given by: where a is the snowfall accumulation. R'(a) = (a+1)a + 2a - 27, (a) Determine the function R(a) given that the ski hill does not open until there has been 7 cm of snowfall (i.e., the revenue is zero when a = 7). (b) Evaluate R(100), and include a conclusion in the context of the problem. Round your result to the nearest thousand. 1