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anonymous
 one year ago
Im lost..
Fundamental Theorem of Calculus.
Why does y have anything to do with g?
Image coming...
anonymous
 one year ago
Im lost.. Fundamental Theorem of Calculus. Why does y have anything to do with g? Image coming...

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Fundamental Theorem of Calculus

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2been a while since I last explained it and there's no good way of putting this in latex so bear with me for a bit

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0cool, thnx, I got all night :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0congrats on the big green 90 :)

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2The Fundamental Theorem of Calculus Let f be continuous on [a,b] . If F is any antiderivative for f on [a,b], then dw:1437913083460:dw

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2because I can't remember the integral with the a b in latex _

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh..so g[t] in this situation is the topmost value of g[x] here.

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2yes... so we need to integrate using the fundamental theorem of calculus

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so ah.. G[a]  G[t] ?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2dw:1437913289210:dw though the integration is a bit different ... it's similar to substituting (sorry it's after 2 am in the morning so I'm a bit burned)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh right on b  a oops

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2dw:1437913376771:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and F is the antiderviative ?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2you're NOT taking antiderivative of g[x] dx .. for the fundamental theorem of calculus .. you are just substituting.. so ... plug in that t inside g[x] (again after hours... I sound off)

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2"ta" should be g[t]g[a]

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2your heading in your file sounds messed up... we're not using odes XD

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2_ oh I see.. at the second part.. there's an initial condition attached. _ when y[a]=0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0gotcha.. so if G is the antiderivative of g[x] then the integration of g[x] is G[t]G[a] and somehow that is going to relate to y'[t] .. Im not sure why, but I'm guessing that possibly because there is something about all derivatives of this kind being equivalent?

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2I'm not sure. At this late at night I can't find the connection x.x but thanks for the congrats messages x.x

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2y'[t] = g[t] ... feels odeish but can't connect....shutting...down..........zzzzzzzzzzzz

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3This is just fundamental theorem of calculus part 1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So indefinite integration gives you an antiderivative. But definite integration requires an indefinite integration to get an antiderivative... and then we use that to find the definite integration as F[b]F[a]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well if it didn't ask me to connect a function y to g.. and I could see how they connect, I think I would be able to answer this. I dont think I can just copy the definition of the fundamental theorem part 1, and expect to walk away with an acceptable grade

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I'm thinking If F is the antiderivative of f then f is a derivative of F therefore if F gives us the function of a curve then f is the rate of change on that curve. The sum of the rate of change on that curve.. gives us the total change on the curve Then we can get all kinds of other results, like the average.. as (sum of change)/(interval width)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the change over the curve... is where the curve ends  where the curve starts

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0F[b]  F[a] end  start

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0or the sum of all the parts.. \[\int\limits_{a}^{b} f[x] dx\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Ok I think I see what you're doing, all you're saying is dw:1437914782360:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes on the top part. ahh .. yes in that I am seeing f as being some kind of derivative to ... something..

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Yes, in that case, that is the fundamental theorem of calculus :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes.. I see it as F'

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Yes, I'm just saying F is an antiderivative of f and if we take the derivative of the antiderivative we get the derivative which is f, that was a lot..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so I could just write the equation as F[t]F[a] as y[t]  y[a] and then it makes sense for y'[t] =g[t]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and y[a]=0 is probably irrelevant ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmm, I wonder why this rule would be sensitive to the sign of the interval.. and I wonder if they need me to explain that too.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I feel like a bloody bird.. this crap makes perfect sense for about 4 minutes, and then I lose it all again.

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3I'm just seeing what you're trying to say so, dw:1437915317312:dw that seems pretty good to me

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes, thats what Im thinking

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3I think that works out

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0awesome ... thanks much.. that makes sense to me too now

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3Haha yeah, and I'm sure others will drop by and check it out as well, but I think that looks good...

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.2:/ so I'm medal less in this post? seems legit. _

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0They should redo this thing medals are bitcoin.

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.3That would be pretty awesome

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Id give you both bitcoin

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ah I think that y[a]=0 clause, must be related to the idea that if y[a] = 0 then there there is nothing to subtract..
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