Question

We are given the following two vector fields. $\mathbf{F} = \begin{bmatrix} 4 \cdot y \cdot z \\ -4 \cdot x \cdot z \\ 3 \cdot e^x \end{bmatrix}$ $\mathbf{H} = \nabla \times \mathbf{F} = \begin{bmatrix} 4 \cdot x \\ 4 \cdot y - 3 \cdot e^x \\ -8 \cdot z \end{bmatrix}$ Let T be the part of the paraboloid $z = 29 - x^2 - y^2$ that lies inside the cylinder $x^2 + y^2 = 25$ What is the flux of H through the surface T with orientation given by positive z-component? $\iint_T \mathbf{H} \cdot d\mathbf{S} = \iint_T \mathbf{H} \cdot \mathbf{N} \, dS = $

          We are given the following two vector fields.
$\mathbf{F} = \begin{bmatrix} 4 \cdot y \cdot z \\ -4 \cdot x \cdot z \\ 3 \cdot e^x \end{bmatrix}$ 
$\mathbf{H} = \nabla \times \mathbf{F} = \begin{bmatrix} 4 \cdot x \\ 4 \cdot y - 3 \cdot e^x \\ -8 \cdot z \end{bmatrix}$
Let T be the part of the paraboloid $z = 29 - x^2 - y^2$ that lies inside the cylinder $x^2 + y^2 = 25$
What is the flux of H through the surface T with orientation given by positive z-component?
$\iint_T \mathbf{H} \cdot d\mathbf{S} = \iint_T \mathbf{H} \cdot \mathbf{N} \, dS = $

We are given the following two vector fields.
𝐅 =
< b m a t r i x >
𝐇 = ∇×𝐅 =
< b m a t r i x >
Let T be the part of the paraboloid z = 29 - x^2 - y^2 that lies inside the cylinder x^2 + y^2 = 25
What is the flux of H through the surface T with orientation given by positive z-component?
𝐇· d𝐒 = 𝐇·𝐍 dS =

Added by Zachary B.

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