Barrons AP Calculus - David Bock
(C) (Why 14? See the solution for question 39.) ...
(C) This is the Mean Value Theorem for Integrals. ...
(D) This is theorem (2). Prove by counterexamples that (A), (B), (C), and (D) are false. ...
(A) This is a restatement of the Fundamental Theorem. In theorem (1), interchange t and x. ...
(D) Apply theorem (1), noting that ...
(E) Let and u = x^2 ; then By the Chain Rule, where theorem (1) is used to find Replace u by x^2. ...
(E) Since dx = −4 sin θ dθ, you get the new integral Use theorem (4) to get the correct answer. ...
(C) Since dx = 2a sec^2 θ dθ, you get 8πa^3 Use the fact that cos^2 θ sec^2 = 1. ...
(D) Use the facts that dx = sin t dt, that t = 0 when x = 0, and that when ...
(E) The expression for L(5) does not multiply the heights of the rectangles by Δx = 0.2 ...
(D) The average value is ...
53. (B) ...
Answers Explained AREA We give below, for each of Questions 1–17, a sketch of the region, and indicate a typical element of area ...
2. (C) ...
3. (A) ...
4. (D) ...
5. (D) ...
6. (C) ...
7. (E) ...
8. (A) ...
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