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Calculus Theorem Question

  1. Mar 22, 2016 #1
    1. The problem statement, all variables and given/known data

    111.png

    Can any body give me hint how to find K if F(x)= 3x+2

    The integral lower part is not the same, , how to deal with his?

    2. Relevant equations


    3. The attempt at a solution

    Please ,I need hint to start
     
    Last edited by a moderator: Mar 22, 2016
  2. jcsd
  3. Mar 22, 2016 #2

    DrClaude

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  4. Mar 22, 2016 #3

    PeroK

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    ... or, why not just integrate what you've been given?
     
  5. Mar 22, 2016 #4

    Ray Vickson

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    What is preventing you from just computing ##\int_2^x (3t + 2) \, dt## and ##\int_8^x (3t + 2) \, dt##?
     
  6. Mar 29, 2016 #5
    Thank you all,

    The point guys is that , first integration is start from 2 and the other one is start from 8.
    Hence if I have only the base 2, the answer will be 3x+2 =3x+2(but the problem is the second base is 8), cant figure out what I missing till now???

    How can I equate them?

    Thanks again
     
  7. Mar 30, 2016 #6

    DrClaude

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    That's not a valid answer for that definite integral.
     
    Last edited: Mar 30, 2016
  8. Mar 30, 2016 #7
    Thanks

    Could you upload refer to examples with X is the boundary of indefinite integral not numbers?
     
  9. Mar 30, 2016 #8

    Samy_A

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    When a math problem proves to be too difficult, it is a good idea to work on it in little pieces.

    Why don't you do as has been suggested above: forget about the exercise itself, and just compute the following integral:
    ##\int_2^x (3t + 2) dt##.

    What result do you get?
     
  10. Mar 30, 2016 #9

    HallsofIvy

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    What, exactly, is your difficulty? Have you been able to find an anti-derivative for 3t+ 2? That is, can you find [itex]\int 3t+ 2 dt[/itex]? What do you get when you substitute the upper and lower bounds and subtract?
     
  11. Mar 30, 2016 #10
    The answer is 3x+2 (right)!!
     
  12. Mar 30, 2016 #11

    Samy_A

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    No.
    Let's go one more step back (as suggested by HallsofIvy): what is the indefinite integral ##\int (3t +2) dt ##?
     
  13. Mar 30, 2016 #12

    Ssnow

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    Sorry, a stupid question but ##F(x)=3x+2## is a primitive of ##f## or it is the ##f## in the integral?
     
  14. Mar 30, 2016 #13

    Samy_A

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    That's not a stupid question, it's a good catch. :oldsmile:
     
  15. Mar 30, 2016 #14

    Ssnow

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    Ah ok because in one case one must apply directly the Fundamental calculus theorem and in the other side one must find before the primitive ... @keewansadeq you must reflect on this ....
     
  16. Mar 30, 2016 #15

    Mark44

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    I noticed that as well. It could be that F is an antiderivative of f, or, as often happens, some posters mix upper and lower case for a single variable name.
    @keewansadeq, did you intend f and F to represent different functions?
     
  17. Mar 30, 2016 #16

    HallsofIvy

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    I assumed it was the integrand because there would not be a specific constant, like 2, in the anti-derivative. If the itegrand is f(x)= 3x+ 2, then the integrand is [itex]F(x)= (3/2)x^2+ 2x+ C[/itex] where C is a constant that will cancel in the definite integral. If the integrand is the constant, 3, then the anti-derivative is 3x+ C, to be evaluated at 2 and x on one side, 8 and x on the other.
     
  18. Mar 30, 2016 #17

    Ssnow

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    @HallsofIvy I have had the same doubt the fact is that it is possible that in the text of the schedule they choose a particular primitive of ##3## with ##c=2##, I don't know because usually with ##F## denotes the primitive ...
     
  19. Mar 31, 2016 #18
    Yes I did, Capital F means anti antiderivative
     
  20. Mar 31, 2016 #19
    Actually,I am very goof in integration,but I am week in Fundamental calculus theorem, it is to me that derivative of integration will be the same function, that why I am confused.

    Thanks all I appreciate
     
  21. Mar 31, 2016 #20
    This is simple

    3(t^2)/2+2t

    But the main problem is with Fundamental calculus theorem
     
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