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hspirdal

[Not game related]Are these solutions correct?

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hspirdal    218
Hi, being a Norwegian student, I'm not sure if the math terms I show is what international readers would expect, but I think it's pretty much readable, except maybe some constant letters may differ.. Anyhow, I would be grateful if anyone could take a quick look and see if my solutions are correct. I know this forum, is mostly for game related stuff, but people here are usually very helpful in general. Ex1) The curve, the x-axis and the y-axis and the line x = 1 delimits an area in the first quadrant. Calculate the exact volume of the body(wrong term?)appearing when it rotates 360 degrees around the x-axis. Solution: Ex2) Solution: Ex3) Solution: Even if one of these only get confirmed due to lack of time or whatever, I'd be very grateful! I'm sorry if I overstep some forum-rules by posting non-game related math questions.

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smc    292
If you plan on formatting or writing mathematical papers in the future the I highly recommend you use TeX/LaTex. btw... your math is readable.

Edit... Second Edit

1. I get the same result with mathematica

3. Mathematica gives me -(8/5)Log(3/2)

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alex_myrpg    351
Hi,

I'll be glad to give you some hints as to your mistakes (no answers though).

1) Simple arithmetic error in evaluation.

2) Looks correct.

3) Keep your modulus signs.

Hopefully you should see the problems immediately now. :)

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hspirdal    218
Thank you both for showing interest and helping, it is very much appreciated!

Fingon:
Thanks for spotting that error in ex1, the resulting volume should be 4Pi if I'm not terribly mistaken.
I'm not exactly sure what you mean by modulus sign, but I think you mean that LN(a) is always measured as an absolute value and therefor a ln(-2) would be evaluated as ln(2) instead. Is this true for imaginary calculations as well?

Anyhow, here's my updated Exercise 3:


Thanks guys, and good night!

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grhodes_at_work    1385
All,

Thank you for paying attention to the forum rules! This thread is a perfectly fine schoolwork thread.

hspirdal, your post is good. I'm glad that you told us that these were problems for school and asked only for a confirmation, and no corrected solution. The forum really exists for game development discussions, but schoolwork questions are permitted with some conditions, conditions that you met.

Fingon and smc, thank you for giving hspirdal enough information to find the correct solutions while not giving an explicit correction.

This is, to me, a good interchange. The original poster gets some help but is ultimately has to solve the problem independently!

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alex_myrpg    351
grhodes_at_work:
Good to know we were within the rules... The original poster was honest about things and not demanding, so I figured it would be acceptable.

hspirdal:
Sorry, your first answer for question 1 was in fact correct. The typo of the power in the denominator of 2 (instead of 3) caught me out!

Your third solution is now also right, though to be strict you should keep the moduli (absolute value) signs when combining the logs.

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hspirdal    218
grhodes_at_work: I'm glad I wasn't stepping on someones toes by asking my questions. Gamedev.net is certainly a very helpful community.

Quote:
Sorry, your first answer for question 1 was in fact correct.

Fingon: I'm pretty sure my latest solution to Ex1 is the correct one (4pi).
(-16pi)/(12) - (-16pi)/3 = -4pi/3-(-16pi/3)=4pi. In my first solution, I think I mistyped -2pi/3 instead of -4pi/3 and evaluated from there.

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alex_myrpg    351
Quote:
Quote:
Sorry, your first answer for question 1 was in fact correct.

Fingon: I'm pretty sure my latest solution to Ex1 is the correct one (4pi).
(-16pi)/(12) - (-16pi)/3 = -4pi/3-(-16pi/3)=4pi. In my first solution, I think I mistyped -2pi/3 instead of -4pi/3 and evaluated from there.


It *would* be if there were actually meant to be a square term on the bottom. I originally though the same until I realised that your cube term changed into a square term (by a typo?) from the end of the 2nd line to the start of the 3rd. Just redo the integration and you'll see that your original answer was in fact correct. :)

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hspirdal    218
You are very correct, Fingon! I also wrote it off as a typo, when the typo really is the square. A little back and forth, should make for a more solid experience, however. Nice catch! :)

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