Problem with a triple integral in cylindrical coordinates

[Amaelle]

Homework Statement

look at the image

Relevant Equations

cylindrical coordinates

Good day

here is the solution

J just don't understand why the solution r=√2 has been omitted??
many thanks in advance
best regards!

 

[BvU]

Easiest thing to do is make a drawing.
Plane z = 0 :

 

[Amaelle]

thanks a lot and then? why sqrt(2) has been omitted?

 

[Charles Link]

The region needs to be "below" the half-sphere and "above" the paraboloid.

 

[Amaelle]

thanks a million , you nail it!

 

[Amaelle]

Easiest thing to do is make a drawing.
Plane z = 0 :

View attachment 277967

thanks a million your graph with the explantion of Charle link is just awsome!