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## Homework Statement

can you explain this conversion, I am not sure.

Rectangle coord :

[tex]\int^{2}_{-2}[/tex][tex]\int^{sqrt(4-x^2)}_{-sqrt(4-x^2)}[/tex][tex]\int^{2}_{sqrt(x^2 + y^2 )}[/tex] F(x) dzdydx

=

cylindrical coord :

[tex]\int^{2\pi}_{0}[/tex][tex]\int^{2}_{0}[/tex][tex]\int^{2i}_{r}[/tex] r*dzdrd[tex]\theta[/tex]

I see that x^2 + y^2 = r so the right most integral in cylindrical coordinate is from 2 to r

The middle integral from symmetry runs from 0 to sqrt(4 - x^2), but they have that as 0 to 2

So I am assumming this is what they did :

y = sqrt(4-x^2)

y^2 = 4 - x^2

y^2 + x^2 = 4

r = 2

thus, 0<= r <= 2 ?

and the 0 to 2Pi is just the while circle thats begin read.

Also in the rectangle coordinate, what happened to -2 and 2 in the leftmost integral?