A verify that the force field f x y 2 x cos y i cos y

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(a) Verify that the force field F ( x, y ) = (2 x cos y ) i + (cos y - x 2 sin y ) j is conservative. (b) Find a potential function φ ( x, y ) for F ( x, y ). (c) Find the work done by the force field F ( x, y ) along the curve x = t 2 + 1 2 , y = t , 0 t π 2 .
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EGR 265, Spring 2011, Final Exam 8 Problem 9 (10 points) Find the double integral of the function f ( x, y ) = x 3 y 2 over the triangle in the xy -plane with vertices (0 , 0), (1 , - 1) and (1 , 1). Problem 10 (10 points) A lamina of density ρ ( x, y ) = 1 + x + y occupies the half disk R that lies above the x -axis within the circle r = 2. Find the mass of the lamina.
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EGR 265, Spring 2011, Final Exam 9 Problem 11 (6 points Bonus) The function f ( x, y ) = 2 x 2 + y 2 - 3 x is defined on the unit disk x 2 + y 2 1 and takes its maximum value and minimum value at two different points of the disk. Find the two points and the maximum and minimum values.
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