mono

SteamID64: 76561198152395362
SteamID32: [U:1:192129634]
SteamID: STEAM_0:0:96064817
CommunityURL: https://steamcommunity.com/id/nmto/
ProfileURL: https://steamcommunity.com/profiles/76561198152395362

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Privacy: Public
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Premium: UNK

Creation: 2014-08-30 16:15:47 (GMT)
Last Updated: 2024-04-04 22:36:22

VAC Banned: False
Community Banned: False
Game Banned: False
Trade Banned: False

Persona History

NameTime Changed
mono2018-05-21 16:18:00
nmto2017-07-29 17:40:01
nmto !2015-08-19 07:31:02
heir to the monado2014-10-12 10:46:03
TheSuperPaperMario2014-08-30 16:40:04

RealName History

RealNameTime Changed
Ahmad2024-04-04 22:36:22

URL History

URLTime Changed
https://steamcommunity.com/id/nmto/2024-04-04 22:36:22

Avatar History

Privacy History

StateTime Changed
Public2024-04-04 22:36:22 [Estimated]

Comments

Total: [7] | Deleted: [0]

CommenterMessageTimestamp
fruit(•ˋ _ ˊ•)2023-08-26 14:40:43
fruitEvaluate the line integral where C is the given curve. We're integrating over the curve C, y to the third ds, and C is the curve with parametric equations x = t cubed, y = t. We're going from t = 0 to t = 2. So we're going to integrate over that curve C of y to the third ds. We're going to convert everything into our parameter t in terms of our parameter t. So I'm going to be integrating from t = 0 to t = 2. Those will be my limits of integration. Now y is equal to t, so I'm going to replace y with what it's equal to in terms of t. So I'm going to be integrating the function t to the third. Now ds we're going to write as a square root of dx dt squared + dy dt squared, squared of all that as we said dt. So we're integrating now everything with respect to t. So this is going to be equal to the integral from 0 to 2 of t to the third times the square root of -- see the derivative of x with respect to t is 3 t squared. So we have 3 t squared squared + dy dt; well, that's just 1 squared dt.2021-12-21 17:52:38
fruitSo we have the integral from 0 to 2 of t to the third times the square root of 9 t to the fourth + 1 dt. So this is a pretty straightforward integration here. We're going to let u be equal to 9 t to the fourth + 1 then du is equal to 36 t to the third dt and so that tells me I can replace a t to the third dt with a du over 36. And so we're going to have the integral then from -- well, new limits of integration. I'm just going to put some squiggly marks there to remind myself that we switched variables. So I'm not going from t = 0 to t = 2. I'm doing things in terms of you right now. But I have a 1 over 36. I'll put that out front, and we're going to have the square root of u. So u to the 1/2, t to the third dt was replaced by du over 36. We got the 36 out front. And so now this is a pretty easy antiderivative in terms of u. It's u to the 3/2 times 2/3. And again, different limits of integration.2021-12-21 17:52:30
fruitWe could figure out what they are in terms of u, but I'm going to convert back into t. So we're going to have 1 over 36 times 2/3 times u to the 3/2. Now, u is 9 t to the fourth + 1, that to the 3/2 power. And now we can go ahead and go from original limits of integration 0 to 2. So let's see, when I put a 2 in here, we're going to have -- 1 over 36 times 2/3. That's going to be 1 over 54, isn't it? So we'll have 1 over 54 times -- putting a 2 in, we have 9 times 2 to the fourth. That's 9 times 16, which is 144 + 1, is 145. So we put the 2 in there, we get 145 to the 3/2 minus, putting the 0 in, we get 9 x 0 to the fourth. That's 0. 0 + 1 is 1. So we just get 1 to the 3/2 or 1. So let's see, what's the best way to write this. How about 1 over 54 -- I guess we could leave it like that. We could also write 145 to the 3/2 as 145 times the square root of 145 and then minus 1. And that is that line integral of y to the third ds over the given curve C.2021-12-21 17:51:58
Highlander+rep for good music2021-12-21 17:51:44
fruitIn biology class i heard that you could cross dog breeds and get like a labrador - poodle mix and stuff so i tried to make a dane-bulldog mix but all i got was a trip to the ER with bite marks on my rod and a bill for animal abuse my name is dane btw. 😞 Much love from Singapore! 😘2021-12-21 17:50:42
fruit+rep for good music2021-11-28 00:45:05

Friends

Total: [50] | TF2BD: [0] (0.00%) | SB: [2] (4.00%)

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Besowolf
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Financial Stability2018-04-01 16:57:13
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