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cos(e)
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Homework Statement
Let D be the region bounded by x=0, y=0, x+y=1, x+y=4. Using the change on variables x=u-uv, y=uv and the jacobian, evaluate the double integral
double integral of dxdy/(x+y)
Homework Equations
answer is 3
The Attempt at a Solution
i drew the graph and found the boundaries x=1,y=0,x+y=1,x+y=4 and solved u and v for each boundary
for x=0: 0=u-uv
v=1
for y=0: 0=uv
so either v=0 or v=0 or both u and v are 0
for x+y=1: u-uv+uv=1
u=1
for x+y=4: u-uv+uv=4
u=4
therefore i have the region in the uv plane [1,4]X[0,1]
now dx=(1-v)du
dy=udv
therefore i get double integral(i-v)dvdu dudv with v varying from 0 to1 and u varying from 1 to 4 and i get 3/2?
im not sure I am doing the right method, i have a feeling I am wrong when i let y=0 and assume v=0?
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