Results 1 to 14 of 14

Math Help - Repeated integral with dx and dy

  1. #1
    Member
    Joined
    Oct 2010
    Posts
    76

    Repeated integral with dx and dy

    evaluate the following repeated integral

    int(0-pi/2) ( int(y-pi/1) cosysinxdxdy)

    i have never seen a question like this please help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,487
    Thanks
    1391
    This is almost unreadable. Is this \displaystyle \int_0^{\frac{\pi}{2}}{\int_y^{\pi}{\cos{y}\sin{x}  \,dx}\,dy}?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    Just separate it. Here's the middle section.

    \int_{y}^{\pi}\cos(y)\sin(x)dx = \cos(y)\cdot\int_{y}^{\pi}\sin(x)dx

    cos(y) is essentially a constant under and integral in dx.

    Now what?
    Last edited by TKHunny; February 23rd 2011 at 04:05 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Oct 2010
    Posts
    76
    I don't know how to seperate it.

    prove it, yes that is the equation
    sorry my bad typo it is pi/2 in both cases
    Last edited by mr fantastic; February 23rd 2011 at 03:06 AM. Reason: Deleted bad attitude.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,487
    Thanks
    1391
    To start with, evaluate the inner integral...

    \displaystyle \int_y^{\frac{\pi}{2}}{\cos{y}\sin{x}\,dx}.

    Here, since you are integrating w.r.t. \displaystyle x, any function of \displaystyle y is treated as a constant.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Oct 2010
    Posts
    76
    ok but what do you mean by INNER integral?

    i assume from what you've said you are expected to integrate wrt x then integrate the RESULT wrt y? its not the actual differentiation and integration i can't do its understanding what the question is even asking

    to be honest i don't even need to solve the answer its all by the by really, i just want to know whats its asking...
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Oct 2010
    Posts
    76
    im still interested in an answer though i get 0 +cosy am i right
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,487
    Thanks
    1391
    Does it make more sense if it's written like this?

    \displaystyle \int_{0}^{\frac{\pi}{2}}{\left[\int_0^{\frac{\pi}{2}}{\cos{y}\sin{x}\,dx}\right]\,dy}

    Can you see that there is an "inner" integral, which needs to be evaluated first, and an "outer" integral?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Oct 2010
    Posts
    76
    do u work out sin(pi/2) - sin(y) first then integrate or integrate then subtract? i know the top and bottom integral is add and subtract
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Member
    Joined
    Oct 2010
    Posts
    76
    Quote Originally Posted by Prove It View Post
    Does it make more sense if it's written like this?

    \displaystyle \int_{0}^{\frac{\pi}{2}}{\left[\int_0^{\frac{\pi}{2}}{\cos{y}\sin{x}\,dx}\right]\,dy}

    Can you see that there is an "inner" integral, which needs to be evaluated first, and an "outer" integral?
    yes if i saw that question i would know exactly what to do but i didnt realise you could take it in turn like that solve one by one i didnt know that was what u had to do
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Senior Member AllanCuz's Avatar
    Joined
    Apr 2010
    From
    Canada
    Posts
    384
    Thanks
    4
    Quote Originally Posted by mathcore View Post
    ok but what do you mean by INNER integral?

    i assume from what you've said you are expected to integrate wrt x then integrate the RESULT wrt y? its not the actual differentiation and integration i can't do its understanding what the question is even asking

    to be honest i don't even need to solve the answer its all by the by really, i just want to know whats its asking...
    You should review the chapter in your text that deals with multiple integration. Alternatively you can take a gander at the stickied thread at the top of this forum! http://www.mathhelpforum.com/math-he...on-146568.html

    Essentially, if you have a series of integrals you have to evaluate them in the order of most functions in the bounds to least. In other words, if you have an integral of the form,

     \int_a^b \int_{f(x)}^{g(x)} H(x,y)dydx

    You need to evaluate the integral with the bounds dealing with the functions of x first, then evaluate the integral with the constant bounds. Doing it the other way around won't produce a numerical result.
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Member
    Joined
    Oct 2010
    Posts
    76
    Quote Originally Posted by AllanCuz View Post
    You should review the chapter in your text that deals with multiple integration. Alternatively you can take a gander at the stickied thread at the top of this forum! http://www.mathhelpforum.com/math-he...on-146568.html

    Essentially, if you have a series of integrals you have to evaluate them in the order of most functions in the bounds to least. In other words, if you have an integral of the form,

     \int_a^b \int_{f(x)}^{g(x)} H(x,y)dydx

    You need to evaluate the integral with the bounds dealing with the functions of x first, then evaluate the integral with the constant bounds. Doing it the other way around won't produce a numerical result.
    i dont have a 'text' i am not in a college or school

    yourr trying to kill me with that link
    i use what ever resources i can find to learn i am handed these questions and told the websites to look for info
    Follow Math Help Forum on Facebook and Google+

  13. #13
    Senior Member AllanCuz's Avatar
    Joined
    Apr 2010
    From
    Canada
    Posts
    384
    Thanks
    4
    Quote Originally Posted by mathcore View Post
    i dont have a 'text' i am not in a college or school
    i use what ever resources i can find to learn i am handed these questions and told the websites to look for info
    That's not why I posted a link to a turorial on multiple integration or anything.....
    Last edited by mr fantastic; February 23rd 2011 at 03:10 AM.
    Follow Math Help Forum on Facebook and Google+

  14. #14
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    Quote Originally Posted by mathcore View Post
    i didnt realise you could take it in turn like that solve one by one i didnt know that was what u had to do
    It is one of the great results of the calculus, that you CAN do it a piece at a time. Intuition may suggest otherwise for so complex an operation.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Repeated Integral in x and y?
    Posted in the Calculus Forum
    Replies: 12
    Last Post: June 10th 2011, 10:31 PM
  2. Repeated roots
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: October 27th 2010, 04:34 AM
  3. repeated roots
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 7th 2009, 05:51 AM
  4. Replies: 5
    Last Post: January 17th 2009, 02:12 AM
  5. Evaluating a repeated integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 9th 2008, 08:59 AM

Search Tags


/mathhelpforum @mathhelpforum