Need help in finding Limits of Integration (Calc 3)

Need help in finding Limits of Integration!!! :) (Calc 3)

Homework Statement

Evaluate

Integral: f * n dS, where "f" and "n" are vectors and "*" is DOT PRODUCT.

Where,

where
(a) f = (x2, ey, 1),

S: x + y + z = 1, x ≥ 0, y ≥ 0, z ≥

ummm none

The Attempt at a Solution

So, I figured that:
r(u,v) = (u,v,1-u-v)
f (x(u),y(v)) = u2, ev, 1)

I also got N vector, which is 1.

BUT HOW DO I FIND THE INTEGRATION LIMITS?????????!!!!

I know that "x ≥ 0, y ≥ 0, z ≥ ", but how does this help me? Are the integration limits from
0 to INFINITY?

PLease Help!!! I have been trying to think for 48 hours on this!!

THanks!!

hunt_mat
Homework Helper

The normal isn't 1, it's a vector, so it'll have compenents, what is the vector. You're integrating over a surface S, what is this surface?

Delta2
Homework Helper
Gold Member

The integration limits are for x and y from 0 to infinite and for z equal to 1-x-y. Since f doesnt depend on z this doesnt matter.

n is the vector with magnitude 1 and direction normal to the surface x+y+z=1.

Find a way to express n in (a,b,c) notation and the element of surface dS as a function of dx and dy. Then $$f*n=ax^2+be^y+c$$.

dS will be dS=cdxdy.

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