Question 2.2 (11 marks) Consider the function f : R - R with f(x) = -2(x - 3) (x2 + 1). a) Determine an antiderivative of f (x). b) Describe the area of the region {(x, y) ER2 : x 2 -1 and 0 0 such that the following holds: the region that is bounded by the y-axis, the plot of f (x), and the plot of the linear function g: R -> R with g(x) = ax, has area exactly 6. Determine the value of a. Tip: While not necessary for solving Q2.2d), you are allowed to use the WolframAlpha command solve to get numerical solutions to polynomial equations: for example, typing solve x 2-3=7 gives you the solutions v10. Mention WolframAlpha in your solution if you use it. e) Look at the function h: R - R with h(x) = x9 + x7 + 25 + x3 + x. Explain in detail without determining an antiderivative of h(x) why we must have f_, h(x) dx = 0 for every b 2 0