Question

Need help with a double integral. Problem in comments. :)

Answer 1

\[\int\limits_{}^{}\int\limits_{}^{} 2xydxdy\]
Over D={(x,y);2<=x<=3,sqrt(2+x)<=y<=sqrt(6+9x)}

Answer 2

How do I substitute to make a pleasant domain?

Answer 3

Let me help you with that...
\[\Large \iint\limits_R 2xy \ dA\]\[\Large \int\limits_{2}^{3}\int\limits_{\sqrt{2+x}}^{\sqrt{6+9x}{}}2xy \ dydx\]
My my, that IS ugly.

Let me stare at it for a while longer...

Answer 4

dx dy is the original eh

Answer 5

:-)

Answer 6

after all x(sqrt(f(x)))^2 is simple enough :)

Answer 7

I don't follow what you're saying. :D

Answer 8

\[\Large \int\limits_{2}^{3}\int\limits_{\sqrt{2+x}}^{\sqrt{6+9x}{}}2xy \ dydx\]
\[\Large \int\limits_{2}^{3}x[(\sqrt{6+9x})^2-(\sqrt{2+x})^2] \ dx\]

sooo, dydx is simple, but your post starts as dxdy

Answer 9

Are you allowed to just do iterated integration like that and throw in the expressions?

Answer 10

that IS what an iterated integartion is ...

Answer 11

I've never done it just throwing in the variables. :D

Answer 12

\[\int_{a}^{b}\int_{q}^{p}~xy~dydx\]
\[\int_{a}^{b}\left[\int_{q}^{p}~xy~dy\right]dx\]
since x is constant wrt.y
\[\int_{a}^{b}x\left[\int_{q}^{p}~y~dy\right]dx\]
\[\int_{a}^{b}x\left[g(p)-g(q)\right]dx\]

Answer 13

the question is the order of integration ... your original is dx then dy, terenz posted it as dy then dx

Answer 14

Does it really make a difference, though? :3
If you even try to integrate with respect to x first, you'll end up with x again... surely that's not how it should happen D:

Answer 15

It can be dydx if you so like as the domain is not inserted yet.

Answer 16

Something along the lines of multiplication is commutative... not sure if it works with differentials such as dy and dx though, but meh :/

Answer 17

the order makes a difference most of the time yes. that is why when you swap the order you have to reassess the limits

Answer 18

i think it has something to do with a Jacobian ...

Answer 19

but if you simply had dA to start with, and your limits were defined, then im sure your original dxdy was just a typing error

Answer 20

The problem says dxdy but when you have not inserted the integration intervals, the order of it doesn't matter; however when you do insert them you have to make sure you have dy corresponding to the right integral.

Answer 21

Unless you can convince me otherwise :D