(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate double integral R of sin((x+y)/2)*cos((x+y)/2), where R is the triangle with vertices (0,0), (2,0), and (1,1) using change of variables u = (x+y)/2 and v = (x-y)/2

2. Relevant equations

Are my integrands correct? I'm getting the wrong answer...the solution is 1 - (sin 2)/2 but I'm getting 1 + (sin2)/2 - 2cos(1)sin(1)

3. The attempt at a solution

(1) Solve for x and y using the change of variables and you get y = u-v and x = u+v. Convert the (x,y) coordinates into (u,v) coordinates and for (u,v) coordinates you get new vertices (0,0), (1,1), and (1,0).

(2) SOlve for the Jacobain factor --> Factor = 2.

(3) Set up the integral: so according to the new triangle in (u,v) coordinates we see that v ranges from 0 to 1 and u ranges from v to 1. So we we have the double integral of where integral of v =(0,1), integral of u = (v,1) sin(u)*cos(v) 2dudv.

I know I have the right set up, but according to the solution, my error lies in setting up the integrals. Please help. I know this is like my 3rd question in two days =(

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Integration using change of vars

**Physics Forums | Science Articles, Homework Help, Discussion**