Discussion
Put these steps of testing a plane field for conservativeness and finding its potential in order. 1. Integrate one component to obtain a candidate potential 2. Compare \( \partial N/\partial x \) with \( \partial M/\partial y \) 3. Differentiate the candidate in the other variable and match the remaining component 4. Write the field as \( M\mathbf{i} + N\mathbf{j} \)
Answer: A
The components are identified first, then the cross-derivative test decides whether a potential exists at all - there is no point integrating if it fails. One component is then integrated, leaving a function of the other variable, which the second component fixes. Integrating before testing is what wastes the effort
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