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mr_coffee

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Hello everyone, this is an example out of the book, but I'm confused on how they got the spheircal cordinates.

Here is the problem:

Evaluate tripple integral over B (x^2+y^2+z^2) dV and use spherical coordinates.

Well the answer is the following:

In spherical coordinates B is represented by {(p,theta,phi)| 0 <= p <= 1, 0 <= theta <= 2pi; 0 <= phi <= pi }; Thus ripple integral of B (x^2+y^2+z^2) dV = tripple intgral (p)^2*p^2 sin(phi) dp d(theta) d(phi)

I'm lost on how they got (p)^2*p^2 sin(phi)

I know the following though,

http://tutorial.math.lamar.edu/AllBrowsers/2415/SphericalCoords_files/eq0020M.gif I figured out how they get the new bounds in spherical coordinates.

But when I used the formula, all i got was

(psin(phi)*cos(theta))^2 + (psin(phi)*sin(theta))^2 + ((pcos(phi))^2; not what they got.

I also saw that: http://tutorial.math.lamar.edu/AllBrowsers/2415/SphericalCoords_files/eq0022M.gif

but this still doesn't explain the extra p^2*sin(phi) it does explain the extra p^2 though.

Any help would be great!

Here is the problem:

Evaluate tripple integral over B (x^2+y^2+z^2) dV and use spherical coordinates.

Well the answer is the following:

In spherical coordinates B is represented by {(p,theta,phi)| 0 <= p <= 1, 0 <= theta <= 2pi; 0 <= phi <= pi }; Thus ripple integral of B (x^2+y^2+z^2) dV = tripple intgral (p)^2*p^2 sin(phi) dp d(theta) d(phi)

I'm lost on how they got (p)^2*p^2 sin(phi)

I know the following though,

http://tutorial.math.lamar.edu/AllBrowsers/2415/SphericalCoords_files/eq0020M.gif I figured out how they get the new bounds in spherical coordinates.

But when I used the formula, all i got was

(psin(phi)*cos(theta))^2 + (psin(phi)*sin(theta))^2 + ((pcos(phi))^2; not what they got.

I also saw that: http://tutorial.math.lamar.edu/AllBrowsers/2415/SphericalCoords_files/eq0022M.gif

but this still doesn't explain the extra p^2*sin(phi) it does explain the extra p^2 though.

Any help would be great!

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