Math 155-004, Quiz 13 May 5, 2009 NAME: Instructions: You may use calculators. Work that is erased or crossed out will not be graded. 1. (2 points) Find the left-hand estimate to the definite integral of the function et from t = 0 to t = 1. Use n = 2. 2. (4 √points) Evaluate the following integrals: R π (a) 0 3t sin(t2 )dt (b) R∞ 1 1 x2 dx 3. (2 points) Find the area under the graph of the curve g(x) = xe2x for 1 ≤ x ≤ 2 (use integration by parts). 4. (2 points) The population p(t) of bunny rabbits in Ingersoll Meadow follows the differential equation dp = 4 + 2 sin(3t), dt and the population at time t = 0 is 100. (a) Express the total change in the population between times t = 0 and t = π3 as a definite integral. (b) Evaluate the definite integral. Extra Credit: The basic model used to analyze the dynamics of infectious disease is a system of .