Vector Analysis Review for Mechanics course

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The discussion focuses on difficulties with integrating a specific sum in a Vector Analysis context for a Mechanics course. The user expresses confusion about their integration process, suggesting they may be making errors. They mention successfully differentiating the right-hand side to obtain the integrand but still struggle with the integration itself. Visual aids are provided to illustrate the problem. Clarification on integration techniques or methods may be needed to resolve the issue.
Shackleford
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Okay. How the heck do I integrate this sum? I have to be doing something wrongly.

http://i111.photobucket.com/albums/n149/camarolt4z28/2010-09-02193820.jpg?t=1283474406

http://i111.photobucket.com/albums/n149/camarolt4z28/2010-09-02192641.jpg?t=1283474140
 
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Well, I differentiated the right-hand side and got the integrand.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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