Exercise · ZW-CONSERVATIVE-FIELD-006 · ★★☆ Intermediate
Compute \(\int_C\mathbf F\cdot d\mathbf r\) with \(\mathbf F=\langle e^y,\,xe^y\rangle\), from \((0,0)\) to \((2,1)\), along any path.
Choose one option.
Show answer
- C. \(2e\)
Explanation
Since \(P_y=e^y=Q_x\), the field is conservative with potential \(f=xe^y\). The integral is \(f(2,1)-f(0,0)=2e\).
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 \(\mathbf F\).
\[\mathbf F=\nabla f\]
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