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Math Help - Multiple integral to check

  1. #1
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    Multiple integral to check

    Could somebody check my solution if it is correct.
    I got the answer -4.
    I don't know if it is right or not.
    Attached Thumbnails Attached Thumbnails Multiple integral to check-topeltintegraal_1.jpg  
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by totalnewbie View Post
    Could somebody check my solution if it is correct.
    I got the answer -4.
    I don't know if it is right or not.
    First observe that the integrand (4-y) is positive on D. Therefore the integral
    over D cannot be negative.

    The region of integration is 0<x<2, x^2/4<y<1, so our integral may be written:

    I = integral_{x=0,2} [integral_{y=x^2/4,1} (4-y) dy] dx

    .. = integral_{x=0,2} [7/2 - x^2 + x^4/32] dx

    .. = 68/15 = 4.533..

    Which agrees with my numerical result using MonteCarlo methods of 4.535.

    RonL
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    First observe that the integrand (4-y) is positive on D. Therefore the integral
    over D cannot be negative.

    The region of integration is 0<x<2, x^2/4<y<1, so our integral may be written:

    I = integral_{x=0,2} [integral_{y=x^2/4,1} (4-y) dy] dx

    .. = integral_{x=0,2} [7/2 - x^2 + x^4/32] dx

    .. = 68/15 = 4.533..

    Which agrees with my numerical result using MonteCarlo methods of 4.535.

    RonL
    Your post came little bit late because I gave my solutions to the teacher today at 10 AM. OK, I will give the correction when the teacher returns my excercise book.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by totalnewbie View Post
    Your post came little bit late because I gave my solutions to the teacher today at 10 AM. OK, I will give the correction when the teacher returns my excercise book.
    Trying to sort out time zones can be a problem online, you have yours
    set up 3 hours east of me, but your ISP appears to be in the Netherlands!?

    But to be brief - When was 10 AM? My post is time stamped 08:11 (AM)
    and your reply 14:09 (02:09 PM) in my time zone.

    OK repeat search - Estonia!

    RonL
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