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anonymous
 one year ago
Example 4 on
http://tutorial.math.lamar.edu/Classes/CalcIII/DIPolarCoords.aspx
Why is this correct? How does subtracting the volume under z = 16 from the volume under z = x^2 + y^2 on a specific radius give us the desired volume?
anonymous
 one year ago
Example 4 on http://tutorial.math.lamar.edu/Classes/CalcIII/DIPolarCoords.aspx Why is this correct? How does subtracting the volume under z = 16 from the volume under z = x^2 + y^2 on a specific radius give us the desired volume?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry dude the link doesn't work....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry, I fixed it now. Yes it is.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wow... I am sorry I can't help. I just started Calculus  I am only in tenth grade. Sorry.

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0you're looking for the volume of the paraboloid itself, ie the volume inside that solid but the normal double integral of the function f, ie\( \iint f(x,y) \ dA \) will give you the volume under the pataboloid, ie the volume from the xy plane upwards

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0handily, though, that volume it does give you can be subtracted from the volume of the cylinder to get the inside volume. and by cylinder i mean the volume under the plane \(z = 16\) within the region \(16 = x^2 + y^2\)

phi
 one year ago
Best ResponseYou've already chosen the best response.0In 2D they are doing this dw:1440248565912:dw that is the integral under the curve f(x)

phi
 one year ago
Best ResponseYou've already chosen the best response.0but if we want the area (or in 3D, the volume) of the "inside" dw:1440248674950:dw

phi
 one year ago
Best ResponseYou've already chosen the best response.0then we find the area of the enclosing rectangle (cylinder in 3D) and subtract off the area of f(x) dw:1440248748282:dw
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