50-Line-Integral-Differential-Form.pdf

You start by finding dy directly from the given path

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You start by finding dy directly from the given path: 2 4 4 2 y x x dy x dx And then transform the line integral so that everything is with respect to x and dx : 4 2 2 1 2 4 2 3 1 4 4 2 69 4 3 2 2 C y dx x dy d x x x dx x x x dx x x   This example illustrates a convenient feature of the line integral in differential form: It allows you to work with the curve C directly without having to find the parametric equation for it . Because you convert the line integral to