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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...

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  1. anonymous
    • one year ago
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    Fundamental Theorem of Calculus

  2. UsukiDoll
    • one year ago
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    been 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

  3. anonymous
    • one year ago
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    cool, thnx, I got all night :)

  4. anonymous
    • one year ago
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    congrats on the big green 90 :)

  5. UsukiDoll
    • one year ago
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    The Fundamental Theorem of Calculus Let f be continuous on [a,b] . If F is any anti-derivative for f on [a,b], then |dw:1437913083460:dw|

  6. UsukiDoll
    • one year ago
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    because I can't remember the integral with the a b in latex -_-

  7. anonymous
    • one year ago
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    oh..so g[t] in this situation is the topmost value of g[x] here.

  8. UsukiDoll
    • one year ago
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    yes... so we need to integrate using the fundamental theorem of calculus

  9. anonymous
    • one year ago
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    so ah.. G[a] - G[t] ?

  10. UsukiDoll
    • one year ago
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    |dw: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)

  11. UsukiDoll
    • one year ago
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    that's backwards

  12. anonymous
    • one year ago
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    oh right on b - a oops

  13. UsukiDoll
    • one year ago
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    |dw:1437913376771:dw|

  14. anonymous
    • one year ago
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    t - a

  15. anonymous
    • one year ago
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    and F is the antiderviative ?

  16. UsukiDoll
    • one year ago
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    you'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)

  17. UsukiDoll
    • one year ago
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    "t-a" should be g[t]-g[a]

  18. UsukiDoll
    • one year ago
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    your heading in your file sounds messed up... we're not using odes XD

  19. UsukiDoll
    • one year ago
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    -_- oh I see.. at the second part.. there's an initial condition attached. -_- when y[a]=0

  20. anonymous
    • one year ago
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    gotcha.. 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?

  21. UsukiDoll
    • one year ago
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    I'm not sure. At this late at night I can't find the connection x.x but thanks for the congrats messages x.x

  22. UsukiDoll
    • one year ago
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    y'[t] = g[t] ... feels odeish but can't connect....shutting...down..........zzzzzzzzzzzz

  23. Astrophysics
    • one year ago
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    This is just fundamental theorem of calculus part 1

  24. anonymous
    • one year ago
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    So 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]

  25. anonymous
    • one year ago
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    well 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

  26. anonymous
    • one year ago
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    Ok..

  27. anonymous
    • one year ago
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    So 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)

  28. anonymous
    • one year ago
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    So the change over the curve... is where the curve ends - where the curve starts

  29. anonymous
    • one year ago
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    F[b] - F[a] end - start

  30. anonymous
    • one year ago
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    or the sum of all the parts.. \[\int\limits_{a}^{b} f[x] dx\]

  31. anonymous
    • one year ago
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    of change that is.

  32. Astrophysics
    • one year ago
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    Ok I think I see what you're doing, all you're saying is |dw:1437914782360:dw|

  33. anonymous
    • one year ago
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    Yes on the top part. ahh .. yes in that I am seeing f as being some kind of derivative to ... something..

  34. Astrophysics
    • one year ago
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    Yes, in that case, that is the fundamental theorem of calculus :)

  35. anonymous
    • one year ago
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    yes.. I see it as F'

  36. Astrophysics
    • one year ago
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    Yes, 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..

  37. anonymous
    • one year ago
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    so 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]

  38. anonymous
    • one year ago
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    and y[a]=0 is probably irrelevant ?

  39. anonymous
    • one year ago
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    hmm, 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.

  40. anonymous
    • one year ago
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    I feel like a bloody bird.. this crap makes perfect sense for about 4 minutes, and then I lose it all again.

  41. Astrophysics
    • one year ago
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    I'm just seeing what you're trying to say so, |dw:1437915317312:dw| that seems pretty good to me

  42. anonymous
    • one year ago
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    yes, thats what Im thinking

  43. Astrophysics
    • one year ago
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    I think that works out

  44. anonymous
    • one year ago
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    awesome ... thanks much.. that makes sense to me too now

  45. Astrophysics
    • one year ago
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    Haha yeah, and I'm sure others will drop by and check it out as well, but I think that looks good...

  46. UsukiDoll
    • one year ago
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    :/ so I'm medal less in this post? seems legit. -_-

  47. Astrophysics
    • one year ago
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    But your 90!

  48. anonymous
    • one year ago
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    They should redo this thing medals are bitcoin.

  49. Astrophysics
    • one year ago
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    That would be pretty awesome

  50. anonymous
    • one year ago
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    Id give you both bitcoin

  51. anonymous
    • one year ago
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    Ah 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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