1a) suppose we want to integrate a funciton f(x,y) over the ellipse x^2/a^2 + y^2/b^2=1 (where a is not equal to b are positive constants). Suggest a suitable change of variables, and find the Jacobian of this transformation. (use a modified version of polar coordinates) b) Using the answer to (a), find the volume of the region enclosed beneath the elliptic paraboloid z = 12-x^2-3y^2 and above the xy-plane.

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I have no idea where to start. I tried to convert the coordinates into polar coordinates (x=rcos(theta), y=rsin(theta). I don't know even where to start...

A much better parameterization would be x = a cos (theta), y = b* sin(theta)

okay so, I have donethat and got the determinant of the jacobian =abr how do i do part 2?....

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