Egrma 265 final exam 8 problem 8 12 points a is the

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EGR/MA 265, FINAL EXAM 8 Problem 8 (12 points) (a) Is the force field F ( x, y ) = 3 x 2 y 4 i +4 x 3 y 3 j conservative? If your answer is yes, then find a potential function Φ( x, y ) for it. (b) Find the work done by the force field F from part (a) along a portion of the parabola given by the parametric equations x ( t ) = t , y = t 2 , 0 t 1.
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EGR/MA 265, FINAL EXAM 9 Problem 9 (10 points) A lamina of constant density ρ ( x, y ) = 1 is bounded by the curves x = y 2 - 1 and x = 0. (a) Find the lamina’s mass. (b) Find the lamina’s centroid. Use geometric considerations to simplify your work.
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EGR/MA 265, FINAL EXAM 10 Problem 10 (10 points) Find the double integral of the function f ( x, y ) = x 2 + y 2 over the region in the second quadrant which is bounded by the circles r = 2 and r = 4.
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EGR/MA 265, FINAL EXAM 11 SCRATCH PAPER
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EGR/MA 265, FINAL EXAM 12 SCRATCH PAPER
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