Exercise · ZW-CONSERVATIVE-FIELD-004 · ★☆☆ Basic
Find a potential of \(\mathbf F=\langle 2x+y,\;x+2y\rangle\).
Choose one option.
Show answer
- D. \(f=x^2+xy+y^2\)
Explanation
Integrating \(f_x=2x+y\) gives \(x^2+xy+g(y)\); differentiating in \(y\) and comparing with \(x+2y\) forces \(g=y^2\). Check: \(\nabla f=\langle2x+y,x+2y\rangle\).
Review the concept: Conservative field
A vector field \(\mathbf F\) is conservative if it is the gradient of a scalar function \(f\), called a potential function of \(\mathbf F\).
\[\mathbf F=\nabla f\]
More practice problems: conservative field
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