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Hello, I've got a problem which I am just stuck with..:
[Triple integral]D x^2+y^2 dxdydz, where D: 0<=x^2+y^2<=z^2 , 0<=z<=1
I have tried with spherical coordinates and other stuff(/tricks). I think my problem maybe is in dealing with the intervals. Could somebody please help me with at least some hints?
Sorry if there is something missing in my post. This is my first post on this forum. hehe
Thanks in advance!
Are you clear that D is just a circular cone with a = 1 and h = 1? Cylindrical...
z is going...
from z = r (the side of the cone) up to z = 1 (the base)
... for every bit that r is going...
from zero (the z axis) along to as far as where r = z = 1
... for every bit that theta is going right round (zero to 2 pi).
And your integrand is r(x^2 + y^2) = r^3.
Yes, cylindrical coordinates is the way to go.
Thank you! Solved it!