Question
Asked Nov 3, 2019

I get how to do the problem up until ∫∫[u(u+v-u)] 

 

where did they get [u(u+v-u)]  from? Please explain 

Evaluating a Double Integral Using a Change
of Variables In Exercises 17-22, use the
indicated change of variables to evaluate the
double integral
У(х — у)dA
х%3D и — и
y u
6
4
(3, 3)
(7, 3)
2
x
(0, 0) (4, 0) 6 8
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Evaluating a Double Integral Using a Change of Variables In Exercises 17-22, use the indicated change of variables to evaluate the double integral У(х — у)dA х%3D и — и y u 6 4 (3, 3) (7, 3) 2 x (0, 0) (4, 0) 6 8

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y (x- y)lu (u + v- u)] |;
S(x.y)
S(u.v)
dvdu
R
ue]- dedu
0
0
3
du
2.
=8udu
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y (x- y)lu (u + v- u)] |; S(x.y) S(u.v) dvdu R ue]- dedu 0 0 3 du 2. =8udu

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check_circleExpert Solution
Step 1

To determine the double integral using a suitable change of coordinates

Step 2

The region in x,y coordinates (bounded by the red lines)

в
2
1
3
5
7
С
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в 2 1 3 5 7 С

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Step 3

Consider the map x=u-v,y=v  (SEE correction). This is equivalent to u=x-y, v=y. The points O,A, B, C get transformed to O,P,Q, R as shown in the graph. For examplel...

5
P
2
8
0-
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5 P 2 8 0-

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Advanced Math