The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

Surface integral question

So I need to evaluate ∫∫S.(x+y+z)dS\int \int_{S}^{.}(x+y+z)dS where S is the surface 6x+3y+2z=6,x,y,z≥06x+3y+2z=6,x,y,z\geq 0.

For some reason, I have written down this is:
72∫02∫0y(−2x−y2−3)dxdy\frac{7}{2}\int_{0}^{2}\int_{0}^{y}(-2x-\frac{y}{2}-3)dxdy

but I can't remember why I did the top limit of the x integral as y? Should it not be 1-y/2?

(http://www.wolframalpha.com/input/?i=6x%2B3y%3D6 this is the region I'm integrating over)

Should it be 1-y/2?
If it is y, why? [If I do it as y, I get a very nice answer in the end!]

If required, I can post a photo of all of my working!
(edited 9 years ago)
Reply 1
Avatar for TeeEm
TeeEm
19
Original post by rayquaza17
So I need to evaluate ∫∫S.(x+y+z)dS\int \int_{S}^{.}(x+y+z)dS where S is the surface 6x+3y+2z=6,x,y,z≥06x+3y+2z=6,x,y,z\geq 0.

For some reason, I have written down this is:
72∫02∫0y(−2x−y2−3)dxdy\frac{7}{2}\int_{0}^{2}\int_{0}^{y}(-2x-\frac{y}{2}-3)dxdy

but I can't remember why I did the top limit of the x integral as y? Should it not be 1-y/2?

(http://www.wolframalpha.com/input/?i=6x%2B3y%3D6 this is the region I'm integrating over)

Should it be 1-y/2?
If it is y, why? [If I do it as y, I get a very nice answer in the end!]

If required, I can post a photo of all of my working!



I have not checked the question but you are projecting onto the xy plane, on the triangle bounded by the line 6x+3y=6

i.e 1st quadrant y = -2x+2

can you see the limits from there/

I got final answer 7

Also I think in the integrand it should be +3
(edited 9 years ago)
Reply 2
Avatar for rayquaza17
rayquaza17
OP
17
Original post by TeeEm
I have not checked the question but you are projecting onto the xy plane, on the triangle bounded by the line 6x+3y=6

i.e 1st quadrant y = -2x+2

can you see the limits from there/

I got final answer 7

Also I think in the integrand it should be +3


Oops, I mustn't have held shift down to write the +!

I've done it now, and got 7. (That was the nice answer I suspected it was!)

Much appreciated again, TeeEm. :biggrin:
Reply 3
Avatar for TeeEm
TeeEm
19
Original post by rayquaza17
Oops, I mustn't have held shift down to write the +!

I've done it now, and got 7. (That was the nice answer I suspected it was!)

Much appreciated again, TeeEm. :biggrin:


no worries

(incidentally I have the very same question in my site in the surface integrals booklet)
Reply 4
Avatar for rayquaza17
rayquaza17
OP
17
Original post by TeeEm
no worries

(incidentally I have the very same question in my site in the surface integrals booklet)


Either the questions I'm doing in my vector calc course are common, or something fishy is going on! :eek::tongue:
Reply 5
Avatar for TeeEm
TeeEm
19
Original post by rayquaza17
Either the questions I'm doing in my vector calc course are common, or something fishy is going on! :eek::tongue:


questions repeat I guess

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you