Vault Of Euclid

Work Done by a Conservative Field on a Unit Circle

Multivariable calculus warmup

Calculate the work done by field \( \mathbf{F}(x, y) = \langle 2x, 3y \rangle \) on a particle that traverses the unit circle. Assume the particle begins its movement at \( (-1, 0) \).
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What this problem tests

Tests the student's ability to recognize a conservative vector field and apply its properties to simplify the calculation of a line integral over a closed path.

This problem is typical in a multivariable or vector calculus course when introducing line integrals and conservative vector fields.

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