Results 1 to 9 of 9

Math Help - Integral Question using Fundamental Theorem of Calculus

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    11

    Integral Question using Fundamental Theorem of Calculus

    Hi everyone,

    I am working on this question for calculus, but I am a bit confused by the y's in the range of the integral.

    Here is the question, which asks you to find p'(y).


    I am a bit confused as to what to do next, would subbing 9y for x be all I need to do for this question? (Fundamental theorem of calculus part 1)


    Thanks a lot.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Just plug the "y's" in like they were numbers and your answer will be a function. Here's an example:

    \int_{2y}^{3y}2xdx=(x^2)|_{2y}^{3y}=(3y)^2-(2y)^2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2010
    Posts
    11
    Hi again,

    VonNemo19, wouldn't that be the method for finding the area (definite integral)? I think the question was asking for the derivative of the original function.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    No, the question is asking you to take the integral with respect to x. So, pretend like you don't see the limits of integration (the y's) and find the integral. Then substitute the y's in.

    BTW the fundamental theorem states that \int_a^bf'(x)dx=f(b)-f(a).

    Another example... \int_x^{x^2}(y+y^2)dy=\left(\frac{y^2}{2}+\frac{y^  3}{3}\right)\Big|_x^{x^2}=\left[\frac{(X^2)^2}{2}+\frac{(X^2)^3}{3}\right]-\left[\frac{(X)^2}{2}+\frac{(X)^3}{3}\right]
    Follow Math Help Forum on Facebook and Google+

  5. #5
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Oooppps. Did you just now put that apostrophe in there? p' is very different than p.

    p' is simply...the integrand
    I coulda swore there was no apostrophe there earlier
    Last edited by VonNemo19; November 29th 2010 at 12:34 PM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Example.

    f(x)=\int_y^22xdx=x^2\Big|_y^2=2^2-y^2

    Now, f'(y)=-2y
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2010
    Posts
    11
    Oh, okay thanks!
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,617
    Thanks
    1581
    Awards
    1
    Here is a simple example to show how to do it.

    If p(y) =\displaystyle \int_{8y}^{9y} {(x^2  + 3x - 1)dx} then p'(y) = \left[ {9\left( {(9y)^2  + 3\left( {9y} \right) - 1} \right)} \right] - \left[ {8\left( {(8y)^2  + 3\left( {8y} \right) - 1} \right)} \right]

    Here it idea: if p(y) =\displaystyle \int_{f(y)}^{g(y)} {h(x)dx} then p'(y) = \left[ {h(g(x))g'(x)} \right] - \left[ {h(f(x))f'(x)} \right]<br />
    Follow Math Help Forum on Facebook and Google+

  9. #9
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Dude, I'm really sorry. I messed up like 6 times on this problem. I need to learn how to read better.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: December 11th 2011, 08:00 PM
  2. Replies: 3
    Last Post: July 3rd 2010, 03:43 PM
  3. Fundamental Theorem of Calculus
    Posted in the Calculus Forum
    Replies: 8
    Last Post: July 8th 2009, 06:09 AM
  4. Replies: 2
    Last Post: June 14th 2007, 06:35 AM
  5. fundamental theorem of calculus
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 23rd 2006, 06:30 AM

Search Tags


/mathhelpforum @mathhelpforum