Finding the scalar potential function for a conservative vector field // Vector Calculus

The fundamental theorem of line integrals told us that if we knew a vector field was conservative, and thus able to be written as the gradient of a scalar potential function, we could evaluate any line integral almost trivially by just evaluating that potential function at the endpoints. But how do we FIND the scalar potential function? This video introduces that method. First we test that our vector field really is conservative using the test we saw previously. But after we know the method applies, we apply a trick involving alternating integration and differentiation to get a handle on the constants that come up, and ultimately get the scalar potential function. Finally we see an example were we use the potential function  for a specific line integral.

0:00 Goals
1:00 Test for Conservative
2:50 Find Potential Function
9:43 Compute Line Integral

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