# Finding the area of trapezoid area question

1. Mar 18, 2013

### nemesest

(double integral) cos((y-x)/(y+x))dA
Where the double integral is over the region with points (1, 0), (2, 0), (0, 2), and (0, 1).
I think the trapezoid is enclosed by
y+x = 1
y+x = 2
y=0
x=0
How can I use this? Thanks

2. Mar 18, 2013

### economicstyro

Hello nemesest, for this problem, you can make a substitution u=y-x, v=y+x, compute the Jacobian, and express the integral in terms of u and v (don't forget that the final representation of the integral must involve the Jacobian). The result is (3/2)*sin1. Hope that helps :)