please answer the following

+1 (305) 343-6607 -Javier 1 of 2 12Miquel Gutierre AP Calc BC Unit 6 - Improper Integrals - HW 1. Consider the function f (x) = xe-x. a. Find an antiderivative of f. b. Find the value of Jo xf (x) dx, given the fact that for e-x3 dx = Vi 2. Consider the family of functions f (x) = 2_2 , where k is a constant. a. Find the value of k, for k > 0, such that the slope of the line tangent to the graph of f at x = 0 equals 6. b. Fork = -8, find the value of So f(x) dx. C. For k = 1, find the value of fo f (x) dx or show that it diverges. 3. If R is the unbounded region between the graph of y = x(In x) and the x-axis for x 2 3, then the area of R is a. In 3 b. In (In 3)