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Niles
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[SOLVED] Linear algebra and volume of rotational object
I have to show that V(O) = pi * int[f(z)^2]dx when O = {(x,y,z) E R^3 | a =< z =< b, sqrt(x^2+y^2) =< f(z)}.
I have to integrate 3 times with different limits:
V(O) = int [dz, a..b] * int[dr, 0 .. f(z)] * int[dTheta * r, 0..2pi].
Why is it the integral looks like this? I believe it should look like
int[ int [ int [ dr * dTheta * ds]]] with limits as above.
Homework Statement
I have to show that V(O) = pi * int[f(z)^2]dx when O = {(x,y,z) E R^3 | a =< z =< b, sqrt(x^2+y^2) =< f(z)}.
I have to integrate 3 times with different limits:
V(O) = int [dz, a..b] * int[dr, 0 .. f(z)] * int[dTheta * r, 0..2pi].
Why is it the integral looks like this? I believe it should look like
int[ int [ int [ dr * dTheta * ds]]] with limits as above.