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Math Help - Double integral problem

  1. #1
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    Double integral problem

    I'm trying to prove that J=>0. J is defined as the double integral over region R of f(x,y)dA with R = [-2,2]x[2,4] and f = (x^5+y^5)^(1/5). I know I have to set f smaller and bigger than my region R, but then how can I translate that to the integral?
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  2. #2
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    Re: Double integral problem

    Quote Originally Posted by richardsim10 View Post
    I'm trying to prove that J=>0. J is defined as the double integral over region R of f(x,y)dA with R = [-2,2]x[2,4] and f = (x^5+y^5)^(1/5). I know I have to set f smaller and bigger than my region R, but then how can I translate that to the integral?
    The Function will have its absolute minimum on the recangle

    [-2, 2] \times [2,4]

    at the point (-2,2)

    and it will have its absolute max at the point

    (2,4).

    This gives.

    0 \le f(x,y) \le 2\sqrt[5]{33}

    But more importantly why does it have these extreem values
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  3. #3
    Senior Member MaxJasper's Avatar
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    Lightbulb Re: Double integral problem

    Function as a surface:

    f(\text{x},\text{y})\text{=}\left(x^5+y^5\right)^{  \frac{1}{5}}

    Attached Thumbnails Attached Thumbnails Double integral problem-f-x-y-.png  
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