Recent content by Tom31415926535

You make a good point. Here are my steps

Homework Statement Let D be the triangle with vertices (0,0), (1,0) and (0,1). Evaluate: ∫∫exp((y-x)/(y+x))dxdy for D by making the substitutions u=y-x and v=y+x Homework EquationsThe Attempt at a Solution So first I found an equation for y and x respectively: y=(u+v)/2 and x=(v-u)/2 Then...

Okay thanks. So I can conclude that that is the correct surface equation. Therefore: r(y,z)= (y,y,z) G(r(x,z))=(y^2, y^2, z) Then the integral will be: ∫∫(y^2, y^2, z)(1+2y+1)dydz Is my reasoning correct? If yes, how do I determine the terminals? If no, what am I doing incorrectly?

Homework Statement Let G=x^2i+xyj+zk And let S be the surface with points connecting (0,0,0) , (1,1,0) and (2,2,2) Find ∬GdS. (over S) Homework EquationsThe Attempt at a Solution I parametrised the surface and found 0=2x-2y. I’m not sure if this is correct. And I’m also uncertain about...

Homework Statement C is the directed curve forming the triangle (0, 0, 0) to (0, 1, 1) to (1, 1, 1) to (0, 0, 0). Let F=(x,xy,xz) Find ∫F·ds. Homework EquationsThe Attempt at a Solution My intial instinct was to check if it was conservative. Upon calculating: ∇xF=(0,-z,y) I concluded that...

Thanks heaps! That’s very helpful :smile: I’m a little uncertain about how to setup the integral to calculate the volume though. Am I correct in needing to perform a change of variables? If so, what am I doing incorrectly that produces a Jacobean of zero? Thanks :smile:

Homework Statement Let C be the parametrised surface given by Φ(t,θ)=(cosθ/cosht, sinθ/cosht,t−tanht), for 0≤t and 0≤θ<2π Let V be the region in R3 between the plane z = 0 and the surface C. Compute the volume of the region V .Homework EquationsThe Attempt at a Solution I thought I needed...

So would the boundaries be: 0≤z≤x+y 0≤y≤1-x 0≤x≤1

Homework Statement Let G be the region bounded by the planes x=0,y=0,z=0,x+y=1and z=x+y. Homework Equations (a) Find the volume of G by integration. (b) If the region is a solid of uniform density, use triple integration to find its center of mass. The Attempt at a Solution [/B] My...