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Nagisa Maths Thread

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Planck's constant:

--- Quote from: TrueTears on December 24, 2012, 12:42:40 am ---This volume can be found very easily by the following computation:



Why?

--- End quote ---


I had not seen this approach before, but I get it now :)

We are taught to visualise solids of revolution as disks of thickness dy stacked one on top of each other. But this approach suggests that we can visualise the same solid of revolution as cylinders of thickness dx one inside of each other.
I can see that this approach simplifies problems such as this one.
I like.

Nagisa:
Evaluate the integral of

Hancock:
Using integration by parts.



Let

and
and 

=





Using a similar idea, with and

TrueTears:
Spoiler



Let and

So and

Note to work out we have and we need to integrate , but to integrate ln(x) we need to use integration by parts again, so .

In this case let and and you should get

Now back to the original question:

Phy124:
SpoilerUsing integration by parts:



(You can "cancel out" dx's and write dv and du, but for some reason I prefer not to)











Need to work out












aw beaten again  ::)

wow double beaten too haha fuark, gotta lift my game  :P


--- Quote from: Hancock on December 26, 2012, 12:39:56 am ---Couldn't remember how to print fractions and integrals. FUUUUUUUUU

--- End quote ---

I shouldn't have walked off to get food mid-way through :(

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