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Fundamental Theorem Of Calculus problems help

  1. Jan 18, 2013 #1
    Fundamental Theorem Of Calculus problems help!!

    1. The problem statement, all variables and given/known data

    A))))

    Find the derivative of
    g(x)=∫[8x to 4x] (u+7)/(u-4) dx


    B)))
    Use part I of the Fundamental Theorem of Calculus to find the derivative of
    h(x) = ∫[sin(x) to -3] (cos(t^3)+t)dt


    C)))
    F(x) = ∫[ 1 to √3] s^3/(3+5s^4) dx



    2. Relevant equations



    3. The attempt at a solution

    I tried to do
    F(b)b' - F(a)a'
    but I am not confident with my answer.
     
  2. jcsd
  3. Jan 18, 2013 #2

    Mark44

    Staff: Mentor

    Re: Fundamental Theorem Of Calculus problems help!!

    What does part I of the Fundamental Thm. of Calculus say?
     
  4. Jan 18, 2013 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Re: Fundamental Theorem Of Calculus problems help!!

    Are you sure you mean g(x) = ∫[8x to 4x] (u+7)/(u-4) dx in A)? As written, this means
    [tex] g(x) = \int_{8x}^{4x} \frac{u+7}{u-4} \, du .[/tex] (Where you wrote 'dx' I assume you mean 'du'.) The point is: what are the limits, and where they go? If you actually want [tex] g(x) = \int_{4x}^{8x} \frac{u+7}{u-4} \, du, [/tex] you would need to write
    ∫[4x to 8x] (u+7)/(u-4) du. The answers for g'(x) are different in these two cases. Which one do you really mean?
     
  5. Jan 18, 2013 #4
    Re: Fundamental Theorem Of Calculus problems help!!

    It's the second one that you stated.
    here is it:
    81d0f19e743039823206fbcd05a6671.png
     
  6. Jan 18, 2013 #5

    Mark44

    Staff: Mentor

    Re: Fundamental Theorem Of Calculus problems help!!

    Is this problem B?
    You wrote "h(x) = ∫[sin(x) to -3] (cos(t^3)+t)dt"

    From your response to Ray, I think this is the function.

    $$ h(x) = \int_{-3}^{sin(x)}(cos(t^3) + t)dt$$

    Can you work the problem below? This is a little easier, and if you can work it, the one above is only a little harder.
    $$ h(x) = \int_{-3}^x(cos(t^3) + t)dt$$

    Let me ask again, what does the first part of the Fundamental Thm. of Calculus say?


    For problem C you wrote "F(x) = ∫[ 1 to √3] s^3/(3+5s^4) dx"

    I can only guess at what you meant, which might be this:
    $$ F(x) = \int_1^{\sqrt{3}} \frac{s^3}{3 + 5s^4} ds$$

    If this is the problem, it's very easy.
     
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