# Math 251........The end

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- Math 251........The end

**Created:**2014-08-12

**Last Modified:**2014-08-12

1. parameterize the curve.

2. fid Ds (ds is the magnitude of the derivative of the parameterization of the curve)

3. now multiply ds by the function in terms of the parameterization.

4. solve that bitch

how to test for conservativeness

1. pick a part of the vector ( for example gx)

2. integrate with respect to X with the addition of the unknown Y

3. take the derivative with respect to Y

4. set equal to gy.

5.integrate with respect to Y

(note this only works if the field is conservative)

fundamental theorem of line integrals.

double integral of qx-py da

Only works if function is simple and closed and continuous partial derivatives

Steps

1.find qx and py

2. plug it in and put the bounds.

surface integrals (scalar)

1. parameterize the curve.

2.take partials of the parameterization.

3. cross them to get the normal.

4.dot that with the vector in terms of the parameterization.

5. integrate.

_{c}F • dr = ∫∫

_{s}curl(F) • dS

_{S}∫F•NdS = ∫∫

_{E}∫divFdV

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