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Use the divergence theorem to compute the value of fluxintegral SF · dS, where F(x, y, z) = (y3 + 3x)i +(xz + y)j +[z + x4 cos(x2y)]k and S is the area of the re...

Question

Use the divergence theorem to compute the value of fluxintegral SF · dS, where F(x, y, z) = (y3 + 3x)i +(xz + y)j +[z + x4 cos(x2y)]k and S is the area of the region boundedby x2 + y2 = 1,x ≥ 0,y ≥ 0, and 0 ≤ z ≤ 1.

Use the divergence theorem to compute the value of flux integral S F · dS, where F(x, y, z) = (y3 + 3x)i + (xz + y)j + [z + x4 cos(x2y)]k and S is the area of the region bounded by x2 + y2 = 1, x ≥ 0, y ≥ 0, and 0 ≤ z ≤ 1.



Answers

Use the divergence theorem to compute the value of flux integral $\int_{S} \mathbf{F} \cdot d \mathbf{S}$ where $\mathbf{F}(x, y, z)=\left(y^{3}+3 x\right) \mathbf{i}+(x z+y) \mathbf{j}+\left[z+x^{4} \cos \left(x^{2} y\right)\right] \mathbf{k}$ and $S$ is the area of the region bounded by $x^{2}+y^{2}=1, x \geq 0, y \geq 0,$ and $0 \leq z \leq 1$

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Today we're going to solve problem number six your function if equals, right, Zach X. So, Davis, it was the bio directs off by plus, though by the way off said this so by does it off x So, Dave, it was zero, but I was in student double integral over us Have not the years equals printable over W they f the the which is equals zero. So Dublin double over us. If not, the s equals zero. Thank you.

Did you have all proper number 16 hair limits in central polar coordinates. R, are they, doctor? That is zero less than or equal to are less than or it called toe to then zero less than a recorded data. Less than a recorder to buy, then hard square, less than record. Does it less than or equal toe eight minus are square. So double integral over us half dot ds Because for a printable over w they'll dot here is to art square the rest of that square Go on the way plus side exit squares that come up for that plus square toff X square plus nine right square the so which comes to be like zero to do zero toe by our square to eight minus are square zero plus two plus four are days It did data they are, which is equal to 0 to 2 Took Brian do six Indo uh, eight minus are square minus are square the Europe Well, it's going to be like 24 by 0 to 2 four r minus our Cuba the are which is equals 24 by forward into four by two minus 16 by four which is sick was 96 5 double integral f dot ds That standoff a question. Thank you


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