- #1
vorcil
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Homework Statement
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]
Homework Equations
[tex] \int_\script{v} (\mathbf{\nabla . v }) d\tau = \oint_\script{S} \mathbf{v} . d\mathbf{a} [/tex]
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?