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Getting the image of integration

  1. Jul 23, 2010 #1
    How can i get the image of a integral. Say i have a integral function like this
    [tex]
    \int_{\pi/2}^{\pi} \int_{0}^{2} r\sqrt{4-r^2} drd\theta
    [/tex]

    Now i want to see what volume the integral giving me. Which software i have to use for this purpose.

    Thanks
     
  2. jcsd
  3. Jul 23, 2010 #2
    For this particular integral, you can use any software that plots functions of two variables. In this case, I am assuming the third variable is z, as in cylindrical coordinates, and the integral is evaluating the volume under this surface:
    attachment.php?attachmentid=27146&stc=1&d=1279912547.png
    A lot of free software offers this capability, including GraphCalc and Maxima. Note that you can replace r with [itex]\sqrt{x^2+y^2}[/itex] in order to enter the equation as z = f(x, y) if necessary.
     

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  4. Jul 24, 2010 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    That's in polar coordinates with [itex]\theta[/itex] going from [itex]\pi/2[/itex] to [itex]\pi[/itex]- in Cartesian coordinates, that is the second quadrant. r ranges from 0 to 2 so, within the second quadrant, we are within a circle of radius 2. Finally, the upper boundary is [itex]r\sqrt{4- r^2}[/itex] we can put that in Cartesian Coordinates by setting [itex]= \sqrt{x^2+ y^2}[/itex] so that [itex]z= r\sqrt{4- r^2}= \sqrt[x^2+ y^2}\sqrt{4- x^2- y^2}[/itex]. I doubt that is any 'standard' figure.
     
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