## Related questions with answers

Question

Using $\iint_R \nabla^2 w d x d y=\oint_C \frac{\partial w}{\partial n} d s$, evaluate $\oint_C \frac{\partial w}{\partial n} d s$ counterclockwise over the boundary curve $C$ of the region $R$. (Show the details of your work.)

$w=3 x^2 y-y^3+y^2, \quad C: 25 x^2+y^2=25$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 6We know that

$\oint_C \frac{\partial w}{\partial n}ds=\int\int_R \nabla^2 w dx dy$

Further note that

$\nabla^2 w=\nabla \cdot \nabla w$

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