- #1
sandylam966
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find the area of the cylinder x^2+z^2=a^2 that is inside the cylinder x^2+y^2=a^2.
my attempt:
parameterise x^2+z^2=a^2 as a vector r(x,y) = (x,y,(a^2-x^2)^1/2).
using the formula given here : http://tutorial.math.lamar.edu/Classes/CalcIII/SurfaceArea.aspx, I found the surface area = the double integral of a(a^2-x^2)^-1/2 dxdy, over the circle x^2+y^2=a^2 on the x-y plane.
change variables into polar coordinates, so we obtain the double integral of a(a^2-(r cos (u))^2)^-1/2 rdrdu, for 0<r<a, 0<u<2pi.
Solving this i get zero, which doesn't seem right.
where did i go wrong?
my attempt:
parameterise x^2+z^2=a^2 as a vector r(x,y) = (x,y,(a^2-x^2)^1/2).
using the formula given here : http://tutorial.math.lamar.edu/Classes/CalcIII/SurfaceArea.aspx, I found the surface area = the double integral of a(a^2-x^2)^-1/2 dxdy, over the circle x^2+y^2=a^2 on the x-y plane.
change variables into polar coordinates, so we obtain the double integral of a(a^2-(r cos (u))^2)^-1/2 rdrdu, for 0<r<a, 0<u<2pi.
Solving this i get zero, which doesn't seem right.
where did i go wrong?
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