Integration trouble..

ApeXaviour

Right, I was looking over some past exam papers from these science-maths scholarship exams I was looking to do. It's all revision for me but it's been a while. Anyway, skimming over the double integration questions. Now if I recall correctly it's a fairly simple process, integrate the inner bit, then the outer et voila right? Ok ya got a bit more with oddly shaped areas (type I and II etc) and whatnot but it's still pretty straightforward.

I hit a bump, embarrassingly just with the mechanics of integrating itself, I just couldn't damn remember what to do when the question came up like this.

To elaborate, I'd come accross this question:


Now, if I'm doing this correctly I initially ignore the outer nested bits and concentrate on this:


Wtf do I do with that? I put it through mathematica and it comes up with some "null" argument jive.
Skimmed numerous times through all relevant sections of my calculus book (by Anton) to no avail..

Looked at the previous year's question and sure enough there was one just like it:


With no such example in my obviously inferior recommended text I'm left to ask for help.

Cheers
-Dec

SéamusK

Change about the order of integration.
It's really late and I dont seem to have latex installed so I can't put it up here. But if you change the upper and lower limits to 0 -> y/2, and 0 -> 2.
After integrating w.r.t. x you let u =y^3+1 and all that from the leaving cert.
Sorry if that wasn't too helpful.
I'll do it right properly tomorrow.
I'm tired and doing multiple integrals... last june all over.
Good luck with the schols by the way.