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1. OK, so why is this? Well, if I write
AB
times X
2. I'm going to write (
ab
)dudv. OK, so now, my double integral
3. I claim that the product
AB
represents doing first the
4. this is
ab
times the area of the unit disk,
5.
AB
and BA are not the same thing at all.
6. write, in this particular case, that dudv is (1/
ab
)dxdy,
7. then we apply A. That's the same as applying
AB
8. I will get
ab
times double integral over u^2 v^2<1 of du
9. We can start with BX or we can start with
AB
.
10. is
ab
times dudv. OK, so in my double integral,
11. I claim that the product
AB
represents doing first the
12. OK, so I get dudv equals (1/
ab
)dxdy, or equivalently dxdy
13. then I will get the product,
AB
.
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