(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Check the divergence theorem using the function:

[tex] \mathbf{v} = y^2\mathbf{\hat{x}} + (2xy + z^2) \mathbf{\hat{y}} + (2yz)\mathbf{\hat{z}} [/tex]

2. Relevant equations

[tex] \int_\script{v} (\mathbf{\nabla . v }) d\tau = \oint_\script{S} \mathbf{v} . d\mathbf{a} [/tex]

3. The attempt at a solution

taking the dot product it becomes

[tex] \frac{\partial}{\partial x} y^2 \mathbf{\hat{x}} + \frac{\partial}{\partial y} ( 2xy + z^2) \mathbf{\hat{y}} + \frac{\partial}{\partial z} (2yz)\mathbf{\hat{z}} [/tex]

so by only differentiating the certain parts:

i get y^2 + 2x + z^2 + 2y,

however the dot product of del and my vector v, should've been 2(x+y)

how come I've got y^2 and z^2?

does [tex] \frac{\partial}{\partial x} y^2 [/tex] not equal y^2???

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# Homework Help: Divergence Theorem

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