Question B1: Suppose that f(x) = ar3 + br2 + cr + d. (a) Compute da (b) Compute da [f(x)] dx. (c) Compute at If (t) ] dt. Question B2: Suppose that f(x) is continuous on all of R, and that 1, 12, 13, u1, u2, and u3 are real numbers. (a) Use the Fundamental Theorem of Integral Calculus to prove that In. .u3 ru3 f(x)da + f(x) da + f(x) dx = f(x) da + f(x) da + f(x) da Note: Do not do this with an example. Your proof should only use the information given. You do not get to pick what function f(x) is, and you do not get to pick values of l1, 12, 13, u1, u2, and u3. (b) Draw sketches interpreting the LHS and RHS of (a) as sums and differences of areas in the particular case that f(x) = cos(x) + 1, 1 = 0, 12 = 7, 13 = 7, u1 = 4, u2 = 5, and u3 = ST.Question B3: Determine 7x2 + 3.xdx Question B4: Evaluate Question B5: (a) Sketch the curve y = x sin(x) on the domain [-7, 34]. You should indicate all of the key features that we identified from Ist and 2nd derivatives in chapter 4. (b) Use the product rule for derivatives to compute r cos(x). (c) Evaluate / x sin(x) dx. Show how you found this answer. Hint: x sin(x) = (asin(x) - cos(x) ) + cos(x). (d) What are the critical points of F(x) = / x sin(x) dx on [0, 2x]? Note: You can answer (c) without using the result from (d). (e) Compute x sin (x) dx