Well, my problem isn't with the double integral bit, it's just with the integration once I've switched the limits et cetera. The original problem is:
...and I'm told to solve it by changing the order of integration. I get:I know this forum's not here to check my work, but whether my new limits are correct or not, I still don't know how to integrate with respect to y, taking x as a constant.
Can anyone help?
Let's look at a single integral:
Let and .
Now just substitute:
Now just integrate:
Now just resubstitute for :
Take the derivative to clarify:
All you're doing is substituting one type of variable for another. The actual function isn't changed, just the way it's being represented.
It has cancelled out therefore it's disappeared in my mind. I do understand the whole thing, all I didn't get was why that disappeared 'cause no one was telling me where it'd gone. Although this does seem rather more complicated than examples we've done in lectures :S