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Math Help - Double Integration problem

  1. #1
    iva
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    Double Integration problem

    Hi There,
    I hope its ok to post here as i didn't see a group for Integration....

    I have this problem in my studyguide which provides a solution but no working. I cannot figure out the steps to get it. Any help will be very much appreciated.
    Here goes

    Sketch the region R and calculate the doubleIntegral for

    f(x,y)=sin(x+y)

    R={(x,y) | x >=0, y>=0 and x+y =< π} (this last term is pi)

    The answer to this is π ie pi ie 180 degrees.

    I know that with the double integral the first integral must have the constants, but seeing as we have a non-constant for x and y I don't know how to tackle it

    Many thanks

    PS I tried using the math tag but it removed and changed some of the characters
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    make a sketch, you'll be able to do it from there.
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  3. #3
    Senior Member yeKciM's Avatar
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    hm...

    try like this ...



    sorry my bad.... didn't think it please someone delete this post ....
    Last edited by yeKciM; October 16th 2010 at 05:52 AM.
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  4. #4
    iva
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    Thanks, to be honest I don't undestand the solution but possibly can you just explain how you got to your values for the integrals ie:

    for the double integral I thought I could integrate from

    pi-x to 0 for the first one
    and
    pi - y to 0 for the 2nd

    How come were you able to use pi and not pi-x as per the boundary line x+y<=pi ?
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  5. #5
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by iva View Post
    Thanks, to be honest I don't undestand the solution but possibly can you just explain how you got to your values for the integrals ie:

    for the double integral I thought I could integrate from

    pi-x to 0 for the first one
    and
    pi - y to 0 for the 2nd

    How come were you able to use pi and not pi-x as per the boundary line x+y<=pi ?
    sorry for that one up there ...I'm little sleepy

    your line x+y = pi crosses x axis at point "pi" and so and y axis at the point "pi" now only for which type of integration are you preferring you'll do

     \displaystyle \int _0 ^{\pi} dx \int _0 ^{\pi - x } \sin {(x+y) } dy

    or

     \displaystyle \int _0 ^{\pi} dy \int _0 ^{\pi - y } \sin {(x+y) } dx
    Attached Thumbnails Attached Thumbnails Double Integration problem-line_xypi.jpg  
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  6. #6
    iva
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    Ah thanks I get it now , I was the sleepy one. All made sense after you pointed out the intersection of the line with the axis and if i had sketched it properly ( only made a rough drawing ) I would have seen that . Thanks guys!
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