So here I got such integral. How to change the order of integration? I am not asking you for the answer, but what should be the first step?

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- February 17th 2010, 02:47 AMjacekchanging the order of integration
So here I got such integral. How to change the order of integration? I am not asking you for the answer, but what should be the first step?

- February 17th 2010, 02:52 AMProve It
- February 17th 2010, 01:17 PMjacek
so the 'lines' of this are will be:

? - February 17th 2010, 01:31 PMicemanfan
It really helps to draw a picture for this one. If you change the order of integration, you will need two integrals instead of one.

- February 17th 2010, 01:34 PMjacek
Yep, but should I draw it according to these 'lines' above?

- February 17th 2010, 01:42 PMicemanfan
- February 17th 2010, 01:47 PMjacek
That's ok, my teacher did it once only with integrals.

Could you tell me what's the easiest way to draw without calculator? - February 17th 2010, 01:49 PMicemanfan
- February 17th 2010, 02:01 PMjacek
OK. Is is something like this? http://img692.imageshack.us/img692/3816/kolejnosc.png

- February 17th 2010, 02:03 PMicemanfan
- February 17th 2010, 02:07 PMjacek
Hehe, no! I can draw much better, but this is just auxiliary drawing, isn't it? :)

So, I need to divide it into three parts - part of circle on the right, rectangle in the middle, and this parabola part on the the left? - February 17th 2010, 02:09 PMicemanfan
- February 17th 2010, 04:39 PMjacek
Aha, thanks!

What about such integral?

How can I change it? Because it's only a rectangle... - February 17th 2010, 06:00 PMjacek
Anyone? :)