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This leads to problems for me.

Right now we are covering line integrals over conservative vector fields. We are determining whether or not a field is conservative with the curl method.

However, I've solved every problem without it.

I take the vector field, integrate the i component wrt x, the j component wrt y, and decide that way. If they differ by an added constant or a function of the other variable, I add the two integrated functions together.

This has always led me to a function that if I find the gradient of it, I get the vector field.

If it is not conservative, it is apparent early on after viewing the two integrated functions.

However, if the curl method wasn't necessary it would not be presented. Where will my method break down?