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7 10 pts evaluate the double integral r f x y da

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7. [10 pts] Evaluate the double integral R f ( x, y ) dA , where f ( x, y ) = 2 x y , and R is the rectangle with opposite corners at (2 , 2) and (4 , 3).
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Math 1220 - Spring 2011 Exam 2 Page 6 8. Consider the double integral R x 3 y 3 dA , where R is the region bounded by the graphs of y = 0, x = 2, and y = x 3 . (a) [4 pts] Sketch R . (b) [6 pts] Set up the above double integral as two iterated integrals, one for each possible order of integration, but do not evaluate either .
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Math 1220 - Spring 2011 Exam 2 Page 7 9. [12 pts] The population of an infestation of tribbles is growing at a rate proportional to the number of tribbles present. One day after the infestation was spotted, there were 40 tribbles. Three days after, there were 1000. How many were present when the infestation was first spotted?
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Math 1220 - Spring 2011 Exam 2 Page 8 10. [10 pts] Find the general solution to the differential equation dy dt = y ln y . 11. [8 pts] Show that y = Ce x - x - 1, where C is a constant, is a solution to the differential equation dy dx = x + y . Then find the particular solution that satisfies the initial condition y ( - 1) = 1 e .
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