Results 1 to 11 of 11

Math Help - Integration/Differentiation help.

  1. #1
    Junior Member
    Joined
    Nov 2011
    Posts
    61

    Integration/Differentiation help.

    Can someone please explain how I would differentiate this:

    (1-e^(-x^2))(1-e^(-y^2))

    and integrate this:

    24y(1-x-y)

    Regards.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78

    Re: Integration/Differentiation help.

    Quote Originally Posted by Wevans2303 View Post
    Can someone please explain how I would differentiate this:

    (1-e^(-x^2))(1-e^(-y^2))

    and integrate this:

    24y(1-x-y)

    Regards.
    You need to be more specific.

    For the first one are you taking partial derivatives or is y a function of x?

    For the integral what are you integrating with respect to? dx, dy, dA, ds ? please clarify.

    As asked it is impossible to help you with your questions.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2011
    Posts
    61

    Re: Integration/Differentiation help.

    Apologies TES.

    Differentiating w.r.t x and a double integral dydx.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78

    Re: Integration/Differentiation help.

    So for the first question if you have

    f(x,y)=\dfrac{1-e^{-x^2}}{1-e^{-y^2}}

    The partial derivative with respect to x is

    \dfrac{\partial f}{\partial x}=\dfrac{1}{1-e^{-y^2}}\dfrac{\partial }{\partial x} (1-e^{-x^2})= \dfrac{1}{1-e^{-y^2}}(0-e^{-x^2}(-2x))=\dfrac{2xe^{-x^2}}{1-e^{-y^2}}

    For the 2nd one we need to know the domain of integration. What are the limits?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Nov 2011
    Posts
    61

    Re: Integration/Differentiation help.

    Oh god i've totally messed this up.

    It's the other way round, integrate the first differentiate the second, sorry to have wasted your time.

    If you're still in the mood to help, it would be the double integral of 24y(1-x-y ) with limits 0,1 for both x and y.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,035
    Thanks
    49

    Re: Integration/Differentiation help.

    Quote Originally Posted by TheEmptySet View Post
    So for the first question if you have
    f(x,y)=\dfrac{1-e^{-x^2}}{1-e^{-y^2}}
    ... whereas, if y is a function of x...




    ... where (key in spoiler) ...

    Spoiler:


    ... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case x), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).
    But this is wrapped inside each leg of the legs-uncrossed version of...



    ... the product rule, where, again, straight continuous lines are differentiating downwards with respect to x.


    The second...



    I'll maybe change it to use the limits.

    Here we are, then...



    Quote Originally Posted by Wevans2303 View Post
    Oh god i've totally messed this up.

    It's the other way round, integrate the first differentiate the second, sorry to have wasted your time.

    If you're still in the mood to help, it would be the double integral of 24y(1-x-y ) with limits 0,1 for both x and y.
    But that would still be integrating the second?!
    __________________________________________________ __________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Last edited by tom@ballooncalculus; November 15th 2011 at 02:25 PM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Nov 2011
    Posts
    61

    Re: Integration/Differentiation help.

    Quote Originally Posted by tom@ballooncalculus View Post
    ... whereas, if y is a function of x...




    ... where (key in spoiler) ...

    Spoiler:


    ... is the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case x), and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).
    But this is wrapped inside each leg of the legs-uncrossed version of...



    ... the product rule, where, again, straight continuous lines are differentiating downwards with respect to x.


    The second...



    I'll maybe change it to use the limits.

    Here we are, then...





    But that would still be integrating the second?!
    __________________________________________________ __________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    I'm not making a good first impression here am I!

    Sorry, I need help with integrating the first one with limits 0,1 for both x,y and differentiating the second one.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,035
    Thanks
    49

    Re: Integration/Differentiation help.

    Ok, and is your first expression a fraction as TES was guessing? Either way, this looks dodgy (i.e. non-elementary, involving the error function).

    And in the second, is y a function of x?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Nov 2011
    Posts
    61

    Re: Integration/Differentiation help.

    Quote Originally Posted by tom@ballooncalculus View Post
    Ok, and is your first expression a fraction as TES was guessing? Either way, this looks dodgy (i.e. non-elementary, involving the error function).

    And in the second, is y a function of x?
    I need to integrate this (double integration where limits of x are 0,1 and y are 0,1):

    f(x,y) = 1-e^(-x^2)* 1-e^(-y^2) for x >0, y>0

    I need to differentiate this:

    f(x,y) = 24y(1-x-y) x>0,y>0 & x+y<1

    That's all I am given in the questions.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor
    Joined
    Oct 2008
    Posts
    1,035
    Thanks
    49

    Re: Integration/Differentiation help.

    Quote Originally Posted by Wevans2303 View Post
    I need to integrate this (double integration where limits of x are 0,1 and y are 0,1):

    f(x,y) = 1-e^(-x^2)* 1-e^(-y^2) for x >0, y>0
    int 0 to 1 int 0 to 1 &#40;1-e&#94;&#40;-x&#94;2&#41;&#41;&#40;1-e&#94;&#40;-y&#94;2&#41;&#41; dy dx - Wolfram|Alpha

    I.e...




    To differentiate f(x.y) with respect to (e.g.) x, expand and differentiate term by term, treating y as constant.


    __________________________________________________ ____________________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Junior Member
    Joined
    Nov 2011
    Posts
    61

    Re: Integration/Differentiation help.

    Quote Originally Posted by tom@ballooncalculus View Post
    int 0 to 1 int 0 to 1 &#40;1-e&#94;&#40;-x&#94;2&#41;&#41;&#40;1-e&#94;&#40;-y&#94;2&#41;&#41; dy dx - Wolfram|Alpha

    I.e...




    To differentiate f(x.y) with respect to (e.g.) x, expand and differentiate term by term, treating y as constant.
    Thanks for your help, I think I get it now!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. help with integration/differentiation
    Posted in the Calculus Forum
    Replies: 7
    Last Post: November 11th 2010, 02:48 AM
  2. differentiation and integration AGAIN
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 19th 2010, 12:23 AM
  3. Integration/ Differentiation
    Posted in the Calculus Forum
    Replies: 8
    Last Post: November 6th 2009, 05:34 PM
  4. [SOLVED] integration and differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 2nd 2006, 08:31 AM
  5. Differentiation and Integration
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 27th 2006, 10:51 PM

/mathhelpforum @mathhelpforum