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    Surface Area Confusion

    I'm wondering how you got the expression Sqrt[4r^2 + r^2] dr dtheta. I found the magnitude of the cross product to be Sqrt[4r^4 + r^2]. Integrating over r from 0 to 1 and theta from 0 to 2pi gave me (1/6)(-1 +5*Sqrt[5])*pi. The same answer as when I use x=x, y=y, and z=f(x,y)= 9-x^2 -y^2...
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    Surface Area Confusion

    Just had my test on Vector Fields and there was one question which really confused me. It asked to find the surface area of the parabaloid z = 9-x^2 -y^2 which is above the cone z = 8Sqrt[x^2 + y^2]. My memory told me to use the differential in rectangular coordinates and then convert to...
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    Line/Surface Integrals

    The Fundamental Line Theorem is used when the vector field you are integrating the curve over is conservative (curl = 0). A conservative vector field is the gradient of some function so this theorem allows you to just find the original function and take the difference between any two points in...