Exercise · ZW-VECTOR-LINE-INTEGRAL-004 · ★☆☆ Basic
If \(\int_C \mathbf F\cdot d\mathbf r=7\), what is the integral over the same curve traversed in the opposite direction, \(-C\)?
Choose one option.
Show answer
- B. \(-7\)
Explanation
Reversing the orientation flips the sign of \(\mathbf r'\), so the line integral of a vector field changes sign: \(-7\).
Review the concept: Line integral of a vector field
The line integral of a vector field \(\mathbf F\) over an oriented curve \(C\), parametrized by \(\mathbf r(t)\), \(a\le t\le b\), measures the work \(\mathbf F\) does along \(C\).
\[\int_C \mathbf F\cdot d\mathbf r=\int_a^b \mathbf F(\mathbf r(t))\cdot\mathbf r'(t)\,dt\]
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