Results 1 to 14 of 14

Thread: 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
    12,880
    Thanks
    1946
    This is almost unreadable. Is this $\displaystyle \displaystyle \int_0^{\frac{\pi}{2}}{\int_y^{\pi}{\cos{y}\sin{x} \,dx}\,dy}$?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    Thanks
    2
    Just separate it. Here's the middle section.

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

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

    Now what?
    Last edited by TKHunny; Feb 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; Feb 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
    12,880
    Thanks
    1946
    To start with, evaluate the inner integral...

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

    Here, since you are integrating w.r.t. $\displaystyle \displaystyle x$, any function of $\displaystyle \displaystyle y$ 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
    12,880
    Thanks
    1946
    Does it make more sense if it's written like this?

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

    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?

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

    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,

    $\displaystyle \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,

    $\displaystyle \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; Feb 23rd 2011 at 03:10 AM.
    Follow Math Help Forum on Facebook and Google+

  14. #14
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,111
    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: Jun 10th 2011, 10:31 PM
  2. Repeated roots
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Oct 27th 2010, 04:34 AM
  3. repeated roots
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Sep 7th 2009, 05:51 AM
  4. Replies: 5
    Last Post: Jan 17th 2009, 02:12 AM
  5. Evaluating a repeated integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Dec 9th 2008, 08:59 AM

Search Tags


/mathhelpforum @mathhelpforum