Solving Double Integrals: Sketch and Evaluate

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The discussion revolves around evaluating a double integral with specified bounds. Participants express difficulty in starting the problem, with one user suggesting a change in the order of integration as a potential solution. The integral in question is set between the limits of 0 to 2 for x and x^2 to 4 for y. There is a call for clarification on the bounds to facilitate understanding. The conversation highlights the challenges of visualizing the region of integration and finding an effective method to solve the integral.
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double integrals!

Homework Statement



sketch the region of integration then evaluate the double integral



Homework Equations



^{2}_{0}\int^{4}_{x^2}\intxey2dydx


3. The Attempt at a Solution

I can't even see how to start this problem. I've tried integration by parts but got no where! can some one please give me a direction?
 
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Try changing the order of integration, though I couldn't read what your bounds were =[.
 
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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