How do double integrals even work ?
Last edited by Paradoxica; 21 Feb 2016 at 2:54 PM.
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
You're probably clever enough to get the general gist of it (double integration via Cartesian coordinate system) from this image. I'm guessing you just want a rough idea, not a more rigorous construction.
Just imagine throwing in an extra dimension to everything. Instead of 1 dimensional partitions (the subintervals) of a domain, we have 2 dimensional partitions of a region. Instead of taking 2 dimensional 'strips', we have 3 dimensional 'strips'. Instead of swooping over the domain once, we swoop over it twice (once in the x direction, again in the y direction). Instead of finding an 'area', we find a 'volume'.
Typically it's taught in an first course in vector calculus, not linear algebra where matrices tend to live.
The initial treatments tend to be highly elementary in nature and are very much as you have described above. A Year 11 student could compute some double integrals, simply treating them as a "2 questions in 1" style problem.
However, the difficulty usually comes in the construction of the integral and then spotting clever substitutions/manipulations to invoke Fubini or something that will help simplify the computation.
Pretty much. Though for that question we'd use a combination of the polar and cartesian systems to evaluate it.
In the Volumes problem Q14 of 2014 BOS Trials Extension 2, I provided a VERY brief glimpse into evaluating that integral via double integration (Cartesian).
I think I ignored all the volumes questions in the BoS trials...they looked scarier than inequalities and mechanics...
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
Last edited by Paradoxica; 14 Mar 2016 at 10:03 PM.
Prove the following result:
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
Also, this was a perplexing question for a Q2...
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
“Smart people learn from their mistakes. But the real sharp ones learn from the mistakes of others.”
― Brandon Mull
If I am a conic section, then my e = ∞
Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.
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