http://calc3.askbot.com/questions/Open source question and answer forum written in Python and DjangoenCopyright Askbot, 2010-2011.Thu, 17 Jul 2014 13:26:52 -0500http://calc3.askbot.com/question/125/setting-up-double-integrals/I am working on #16 from 15.8 and I'm wondering if I have set up my integrals correctly. The question asks: Evaluate $\int\int x^2 \hspace{2 mm} dA$ over the region in the first quadrant bounded by the hyperbola $xy=16$ and the lines $y=x, y=0$, and $x=8$. I came up with $$\int_4^8\int_{16/x}^x x^2\hspace{2 mm} dydx$$ is this correct?Thu, 17 Jul 2014 12:15:19 -0500http://calc3.askbot.com/question/125/setting-up-double-integrals/http://calc3.askbot.com/question/125/setting-up-double-integrals/?answer=127#post-id-127(This is actually 15.1 #16) After sketching the graph of this, I thought it would be necessary to evaluate two separate integrals and add them together. When you see the graph, and find the intersection point of the two graphs, you get the line x=4. This shows how these two integrals need to be dealt with separately. That left me with evaluating as follows:  $$\int_0^4\int_0^x x^2\hspace{2 mm} dydx + \int_4^8\int_0^{16/x} x^2\hspace{2 mm} dydx$$ This actually turns out to be pretty easy to integrate, it's the set up that is tricky! Hope this helps... COMMENT ADDED: I changed the graphic I had because I had time to play around with it. I think this one is a better representation of what I was trying to show. The left integral is being added to the right. Thu, 17 Jul 2014 13:26:52 -0500http://calc3.askbot.com/question/125/setting-up-double-integrals/?answer=127#post-id-127