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Point) Let S be the part of the plane z = 3y which lies in the first octant; oriented upward_ Evaluate the flux integralI = HIs F. NdS,of the vector field F == 2i +...

Question

Point) Let S be the part of the plane z = 3y which lies in the first octant; oriented upward_ Evaluate the flux integralI = HIs F. NdS,of the vector field F == 2i + 3j + k across the surface S (with N being the unit upward vector normal to the plane)

point) Let S be the part of the plane z = 3 y which lies in the first octant; oriented upward_ Evaluate the flux integral I = HIs F. NdS, of the vector field F == 2i + 3j + k across the surface S (with N being the unit upward vector normal to the plane)



Answers

Find the flux of the vector field $\mathbf{F}$ across $\sigma$ $\mathbf{F}(x, y, z)=x^{2} \mathbf{i}+y x \mathbf{j}+z x \mathbf{k} ; \sigma$ is the portion of the plane $6 x+3 y+2 z=6$ in the first octant, oriented by unit normals with positive components.

I have a problem for 16 could be the flux of the water through the parabolic cylinder using S E A s. Ah, the function f Did you go to a three z squared I plus six j for six x z k using CS and the following limits get the end grow of zero.

This question are the circular region enclosed boy X squared plus y squared equals four. So the reintegration off regions sigma off f got and yes, equals double integration off this region off to Y square minus one DD, which is equal. Double invigoration, off toe order square, Sinus square seat a minus one and our limit zero to Zito to buy and are the hors d zita. So these will be equally for boy.

In this question, the flocks of the vector field f equals X cake and G equal that minus X squared minus y square. So you think the parameter organization X equal article sign Sita and why equal off us are sign Zito So boy or slugs equals bubble integration with Limit zero and FOI zero and boy Order Square Co sign Cedar the R D C That which is equally. See you Bye Cool science See deceit which is equal or multiply integration Theroux 1/2 Our square G r equals zero. So finally the flux was given. Vector field across the surface is equal to see.

Your problem. 43 Given f you go to zero comma zero come and I could fall on and Z equals four minus X minus. Why? On the flux of the following vector field Given the surface. So, captain, anything partials for this function we get See exes. Go. Negative one and c wise, a good negative one. There for the normal is going to be one. Come one, come with one. Then we can set up our and grow over the region. Zero comes those common negative one dot one. Come on, come on. One. And that equals negative. The area of the region and the area of the region is gonna be the base of the triangle, so it's gonna be one half times with times the height. She goto eight and our area is opposite of their the region. So the fox is gonna be negative


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