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Did the book misprint or am I doing something wrong?

  1. Apr 21, 2008 #1
    this is the question
    find the volume of solid under the graph f(x,y) = x+ y above the region y^2 > x and 0 < x < 9

    So pretty much I have the following integral set up

    0 -> 9 dx
    -sqrt(X) -> sqrt (X) dy
    integrating over the function x+y

    However, when I look at the solutions they did the same thing except for their dy, they took it over
    0 -> sqrt (X)

    is that a misprint or did I do something wrong? Because when I think about it, it's pretty much a parabola and nothing is restricting it from taking each end of the region

    Where as the solutions is only taking half the parabola (from 0 to 9 along X axis which is agreed)

    so is the solutions a misprint or did I do something wrong?
  2. jcsd
  3. Apr 21, 2008 #2


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    Unfortunately, it's hard to tell exactly what was intended since you are clearly not copying exactly what the problem said: "the region y^2> x and 0< x< 9" makes no sense. Perhaps they said "the region bounded by y^2= x, x> 0, x< 9"? Or did they possibly say "in the first quadrant"?
  4. Apr 21, 2008 #3
    sorry it's

    Find the volume of the region under the graph f(x,y)= x+y and above the region y^2 < x , 0 < x < 9

    that is all they say
  5. Apr 21, 2008 #4
    If 0<x<9, then 0<y<3,
    so integrate in these limits (x+y) dx dy = 162
  6. Apr 21, 2008 #5

    D H

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    No. You are ignoring that the y limits are a function of x.

    That suggests a misprint or a misreading. Are you sure the problem doesn't say "above the region y^2 < x"? Even then, the y-integral should be from [itex]-\surd x[/itex] to [itex]\surd x[/itex].
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