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Math Help - double integral

  1. #1
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    double integral

    integral from 1 to 2 and integral from 1 to 3 of e^(-(x+y))

    Is there any reference I can go to to refresh my calculus.
    It's been over 10years since I took my Calculus

    Thank you all in advance,
    Judi
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Judi View Post
    integral from 1 to 2 and integral from 1 to 3 of e^(-(x+y))

    Is there any reference I can go to to refresh my calculus.
    It's been over 10years since I took my Calculus

    Thank you all in advance,
    Judi
    By the rules of exponents
    e^{-x-y} = e^{-x} * e^{-y}
    so you can write your integral as separate integrations over x and y:
    Int[e^{-x-y} dx dy] = Int[e^{-x} dx] * Int[e^{-y} dy]

    and

    Int[e^{-x} dx] = -e^x (over the appropriate limits)

    As I don't know which limits go with which variable I can't help any further, but I suspect you can take it from here.

    (I'll let someone else handle the question about references.)

    -Dan
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    Thank you!
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  4. #4
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    Quote Originally Posted by topsquark View Post
    By the rules of exponents
    e^{-x-y} = e^{-x} * e^{-y}
    so you can write your integral as separate integrations over x and y:
    Int[e^{-x-y} dx dy] = Int[e^{-x} dx] * Int[e^{-y} dy]

    and

    Int[e^{-x} dx] = -e^x (over the appropriate limits)

    As I don't know which limits go with which variable I can't help any further, but I suspect you can take it from here.

    (I'll let someone else handle the question about references.)

    -Dan
    As the integrand is separable into a product of two functions one containing
    only one of the variables and the other the remaining variable, and these
    two functions are the same (except for the name of the variable) it does
    not matter which set of limits go with which variable the integral is the same
    which ever way they are allocated to the variables.

    RonL
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by Judi View Post
    in

    Is there any reference I can go to to refresh my calculus.
    It's been over 10years since I took my Calculus
    There are plenty of online resources for calculus one I like is William Chen's
    lecture notes, which you can find here, but a google search for "calculus notes"
    will give you more links that you can shake a stick at.

    If it you want a good text book, I like Morris Klein's Calculus which has the
    advantages of being cheap and good.

    RonL
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    As the integrand is separable into a product of two functions one containing
    only one of the variables and the other the remaining variable, and these
    two functions are the same (except for the name of the variable) it does
    not matter which set of limits go with which variable the integral is the same
    which ever way they are allocated to the variables.

    RonL
    I was just trying to be general. Okay! Okay! I didn't notice that.

    -Dan
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    Thank you guys!
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