What is the double integral for a triangle with vertices (1,1),(2,4),(5,2)?

[jahlin]

Homework Statement

Compute the double integral where the region is a triangle with vertices (1,1),(2,4),(5,2).(please see the attachment)

Homework Equations

double integral((16-2x-3y)1/11)da

The Attempt at a Solution

first i found the equation of the three lines :

(1,1)-->(5,2) y=x(1/4)+3/4
(1,1)-->(2,4) y=3x-2
(2,4)--->(5,2) y=-x(2/3)+16/3

and then i set up the double integral by defining the range of x and y limits.
1<x<2 , x(1/4)+3/4<y<3x-2
2<x<5, (1/4)x+3/4<y<-x(2/3)+16/3

i integrated these 2 integrals but I am not getting the right answer!

 

[vela]

Your set-up sounds correct. Show us what you did when you integrated. Maybe the problem is there.

 

[jahlin]

if the setup sounds good then i will manage to get the right answer by myself. Thanks