Barrons AP Calculus - David Bock
49. (B) ...
50. (C) ...
51. (B) ...
52. (C) ...
53. (A) ...
54. (D) ...
ARC LENGTH (D) From (3), we obtain the length: ...
(D) Note that the curve is symmetric to the x-axis. Use (2). ...
(B) Use (3) to get the integral: ...
IMPROPER INTEGRALS (C) The integrand is discontinuous at x = 1, which is on the interval of integration. ...
(D) The integral in (D) is the sum of two integrals from −1 to 0 and from 0 to 1. (see Example 29 ). Both diverge. Note that (A ...
(E) Choices (A), (C), and (D) can be shown convergent by the Comparison Test; the convergence of (B) is shown in Example 24. ...
Answers Explained (D) Velocity and changes sign both when t = 1 and when t = 3. ...
(A) Since v > 0 for 0 t 2, the distance is equal to ...
(E) The answer is 8. Since the particle reverses direction when t = 2, and v > 0 for t > 2 but v < 0 for t < 2, the ...
(E) so there is no change in position. ...
(B) Since v = sin t is positive on 0 < t 2, the distance covered is sin t dt = 1 − cos 2. ...
6. (D). ...
(D) The velocity v of the car is linear since its acceleration is constant: ...
(D) Since R(0) = 〈0,1〉, c 1 = 0 and c 2 = 1. ...
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