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# surface integral watch

1. okay so trying to find the area of the plane x-2y+5z = 13 cut out by cylinder x^2 + y^2 = 9

please can someone check the following, as I'm fairly unsure of my method here:

project onto x-y

therefore double integral dS changes for double integral (Fx + Fy +1)^1/2 dA

So it is the integral of root 6/5 dA and x goes from -3 to 3, y from -3 to 3

therefore, answer comes out as 36 root 6 /5 ?

thanks!
2. *bump*
3. I'm not clever enough to understand your method but if I've understood the geometry OK you're trying to find the area of an ellipse.

So if I knew the angle the plane makes with the axis of the cylinder, all would be easy.

So I sort of expect a pi in your answer?? Or have I totally missed the point?
4. hmm I see where you are coming from..

not sure what i've done wrong though..
5. should probably have made clear Fx is partial derivative of F wrt x where f(x,y) here just = z
6. Given that I still don't get your method, how would you answer the same question if instead of a cylinder you had a very long cuboid bounded by x=+/- 3 and y=+/- 3?
7. Your partial derivative thing works out to be sqrt(6/5) which is 1/cos(angle between axis and plane) ??

So I'm guessing the answer works out at 9pi.sqrt(6/5) and your answer just has a square/cuboid rather than a circle/cylinder?
8. ahh yes i see!

Thanks!

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