Study guide and
1 practice problem
on:
Green's theorem
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If $\bfF = L(x,y) \bfi + M(x,y) \bfj$ is differentiable inside a closed and positively oriented curve $C$, then $$\oint_C L(x,y) dx + M(x,y) dy = \iint_D \bigl( \partial_x M(x,y) - \partial_y L(x,y) \bigr) dxdy,$$ where $D$ is the region inside $C$.
Related topics
Line integrals
(8 problems)
Multivariable calculus
(147 problems)
Practice problem
Let $C$ be a circle of radius $a$ centered at the origin, traversed counterclockwise. For what nonzero value of $a$ is $\oint_C \bigl(-y + \frac{1}{3} y^3 + x^2 y \bigr) dx = 0$?
Solution
