Problem with a triple integral in cylindrical coordinates

In summary, a triple integral in cylindrical coordinates is a mathematical concept used to find the volume of a three-dimensional object with a cylindrical shape. It involves integrating a function over three variables: the radius, the angle, and the height. The main difference between cylindrical and Cartesian coordinates is the representation of variables and the limits of integration. To set up a triple integral in cylindrical coordinates, you need to determine the limits of integration, convert the function, and use the triple integral formula. Some common challenges include determining limits, converting the function, and setting up the integral correctly. To solve a problem with a triple integral in cylindrical coordinates, you can follow a step-by-step process that involves determining limits, converting the function, setting up the integral, solving
  • #1
Amaelle
310
54
Homework Statement
look at the image
Relevant Equations
cylindrical coordinates
Good day
1613305455230.png

here is the solution
1613305505439.png

1613305575796.png
J just don't understand why the solution r=√2 has been omitted??
many thanks in advance
best regards!
 
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  • #2
Easiest thing to do is make a drawing.
Plane z = 0 :

1613322264143.png
 
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  • #3
thanks a lot and then? why sqrt(2) has been omitted?
 
  • #4
The region needs to be "below" the half-sphere and "above" the paraboloid.
 
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  • #5
thanks a million , you nail it!
 
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  • #6
BvU said:
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!
 
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