Double Integral:Finding the Area of an Line Intersection.

[Patolord]

Homework Statement

Calculate the area of the figure given by these lines.
;x=y
;x=2y
;x+3y=1
;x+3y=2

Homework Equations

This is the intersection.
http://www.wolframalpha.com/input/?i=x=y;x=2y+;x+3y=1+;x+3y=2
http://www4a.wolframalpha.com/Calculate/MSP/MSP27191hcd6420385b0fg300000fg719cb88h13c52?MSPStoreType=image/gif&s=45&w=386.&h=166.&cdf=RangeControl
and i calculate the intesections even tough idk if it's necessary

• x+3y=1 (2/5 ; 1/5)
• x=2y

• x+3y=1 (1/4 ; 1/4)
• x=y

• x+3y=2 (4/5 ; 2/5)
• x=2y

• x+3y=2 (1/2 ; 1/2)
• x=y

The Attempt at a Solution

Ii's a simple problem i believe but I'm very new to this subject and could'nt get my head around the domain i should integrate.

∫∫dxdy = What is the domain to find the area inside the intersection of these lines.

 

[HallsofIvy]

Since your equations are all of the form x= ..., it looks to me like you need to integrate (1- 3y)- 2y from y= 1/5 to y= 1/4, (1- 3y)- y from y= 1/4 to y= 2/5, and (2- 3y)- y from y= 2/5 to y= 1/2.

Do you see why?