[Double integral] Area of a triangle

  • Thread starter Hatmpatn
  • Start date
  • #1
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Hi! I'm stuck with the following problem:

-----------------------------------
Calculate

∫∫ (x-y)*|ln(x+2y)| dxdy

where D is the triangle with corners in the coordinates (0,0), (1,1) and (-3,3)
-----------------------------------

I get the following lines that forms the triangle: y=-x, y=x and y=-1/2*x+3/2

BX4tVDi.jpg


Im thinking that I start with substitution: (x-y)=u and x+2y=v

Which gives me ∫∫ u*|ln(v)| dudv

After that I don't know how to continue. I would like to know which new "intervals" I should do the integral between when I am in my new u- and v-domain?
 

Answers and Replies

  • #2
35,248
11,502
Im thinking that I start with substitution: (x-y)=u and x+2y=v
That gives ugly borders.
I would use u=x-y and v=x+y then your triangle stays a nice rectangular triangle.

In either case, find the coordinates of the corners in the new coordinate system and then set up the integral again.
 

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