Compute the integral by reversing the order of integration

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The discussion centers on a homework problem involving reversing the order of integration for a double integral. The original poster has struggled to determine the correct limits for x and y after spending considerable time on the problem. They have provided links to the problem statement and a graph for reference. The poster is seeking tips or hints to help solve the integral. Assistance is requested to clarify the limits of integration for successful completion of the task.
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Homework Statement



The problem is in the link.

http://img26.imageshack.us/i/80222189.png/

Homework Equations



None.

The Attempt at a Solution



I did not get far. The only thing I got was the graph. Here is the link to that.

http://img813.imageshack.us/f/graphv.png/

I am suppose to reverse the order of integration. However, I am having trouble finding the limits for x and y.

I spent around 8 hours thinking about this problem -.-

Can anyone please help me with this problem?

Thanks.
 
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Anyone got any tips or hints?
 
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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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