Thread: Triple Integrals In Cylindrical Coordinates.

Using cylindrical coordinates, evaluate (OVER R) , where the solid R is bounded by the surfaces and z=5.

OK, I know how to graph these two surfaces, But how in the earth can I find the limits of the integration?
the " " limits:
but what about " " and " " ??!

Originally Posted by TWiX

Using cylindrical coordinates, evaluate (OVER R) , where the solid R is bounded by the surfaces and z=5.

OK, I know how to graph these two surfaces, But how in the earth can I find the limits of the integration?
the " " limits:
but what about " " and " " ??!

the inside integral

The two surfaces intersect giving a circle of radius 5. This is the region for the outer two integrals.

Originally Posted by Danny

the inside integral

The two surfaces intersect giving a circle of radius 5. This is the region for the outer two integrals.

Nyahahahaa
I got it
But there is a little problem
why is it from r to 5 ?
why not from 5 to r ?

Originally Posted by TWiX

Nyahahahaa
I got it
But there is a little problem
why is it from r to 5 ?
why not from 5 to r ?

The cone ( ) is below the plane ( ).

Originally Posted by Danny

The cone ( ) is below the plane ( ).

hmmmm
I did not memorize the shapes
THANK YOU

Originally Posted by TWiX

Nyahahahaa
I got it
But there is a little problem
why is it from r to 5 ?
why not from 5 to r ?

Originally Posted by TWiX

hmmmm
I did not memorize the shapes
THANK YOU

Well, you don't have to memorize the shapes. At (0,0), z= 0 for the cone and z= 5 for the plane. 5> 0.

Also it is neither "from r to 5" nor "from 5 to r". It is "r ranges from 0 to 5".