Question

Another nice problem is attached from
http://saab.org

Answer 1

First thing to do is get an equation that represents the area R

Answer 2

first observation is : S = 2R, that means scaling factor = 2 .. \(\large \mathbb{dxdy =\frac{1}{2}dudv}\)

Answer 3

also det needs to be +- 2
so by guess and check it is easy to arrive at :-
\(u = x + y\)
\(v = x - y\)

then the integral becomes :-

\(\large \mathbb{\int_0^6 \int_{u-6}^0 ue^v \frac{dv du}{2}}\)

Answer 4

http://www.wolframalpha.com/input/?i=int+0+to+6+int+%28u-6%29+to+0+ue%5Ev+1%2F2dvdu

Answer 5

It also ask for computing the integral without change of variables, You can
see the details in the attached solution generated by http://saab.org

Answer 6

wow ! wthout change of variables is also looking shorter :)
dxdy did the magic ! initially i thougth of doing it by dydx by splitting the region into two -3->0 and 0->3. that turned bit lengthy and i gave up... thnks eliassaab :)

Answer 7

Actually i was thinking the same as you, because i failed to remember the jacobian method :S

Answer 8

Jacobian is oly useful for finding the scaling factor right ? which is easy to figure out here from the xy-plane. I dont think it helps in finding u and v functions... ?

Answer 9

YW @ganeshie8