1st integral is 0 to (innermost)

2nd integral is 0 to

3rd integral is 0 to 1 (outermost)

plse help me out

having trouble inputing question hope this is clear

i am having trouble converting this rectangular triple integral to spherical integrals

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- Apr 28th 2011, 02:08 AMgl7converting rectangular coord. to spherical coord. II

1st integral is 0 to (innermost)

2nd integral is 0 to

3rd integral is 0 to 1 (outermost)

plse help me out

having trouble inputing question hope this is clear

i am having trouble converting this rectangular triple integral to spherical integrals - Apr 28th 2011, 08:06 AMTheEmptySet
You need to listen to your own title!!

You are NOT using spherical coordinates!

Waring 1: Depending on which text you are using and your prof. the representation of spherical coordinates will be different here I will use

Where is the plane angle and is the angle measured from the positive z axis.

So in Spherical coordinates the integrand is

why don't we need an absolute value?

Now Sketch the region of integration and you will see the it is the top half of a sphere of radius 1.

Now to trace a sphere is radius 1

Don't forget to change the differential of volume to spherical coordinates as well.

Fixed my typo above Thanks Ackbeet - Apr 28th 2011, 08:14 AMAckbeet
In which case you should have

The angle appearing in the variable is always the polar angle (measured down from the -axis) and the angle not appearing in is always the azimuthal angle (measured in the -plane, counter-clockwise from the -axis).

Quote:

So in Spherical coordinates the integrand is

why don't we need an absolute value?

Now Sketch the region of integration and you will see the it is the top half of a sphere of radius 1.

Now to trace a sphere is radius 1

Don't forget to change the differential of volume to spherical coordinates as well.