'  File: XIX_dblinteg1  Find the Mass, Center-of-Mass and the Moments of Inertia.

a = 0 :  b = 1 : n = 50  :  m =50  : F{x,y} = 1 :  C{x} = x^3  :  D{x} =x^(1/3)

ma = dblInt[F, C,D, {a,b,n,m,y}]
' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
' Plot the region of interest.
A<x> = <x, C, 0>
B<x> = <x, D, 0>
Plot[A, B, {x, 0,1,50}]
' - - - - - - - - - - - - - - - - - Find the Center of Mass - - - - - - - - - - - - - - - - - - - -
Gx{x,y} = x / ma    :     xm = dblInt[Gx,C,D,{a,b,n,m,y}]
Gy{x,y} = y / ma    :     ym = dblInt[Gy,C,D, {a,b,n,m,y}]

' - - - - - - - - - - - - - - - - - Find the Monents of Inertia (Remove ' comment- - - - - - - - -
'Mx{x,y} = y^2        :       ix = dblInt[Mx,C,D, {a,b,n,m,y}]    ' Ans: 2/15
'My{x,y} = x^2        :       iy = dblInt[My,C,D, {a,b,n,m,y}]    ' Ans: 2/15

' Set up the results to be displayed.!
'@Mass = @ma, = 1/2 exact!
'@Xm = @xm, = 16/35 exact!
'@Ym = @ym, = 16/35 exact!

' Because of 3 sets of analysis, this worksheet will take about 1.5 minutes (on my norebook)!
'   where the average time on most of the other worksheets use around 15 seconds to!
'   about one minute.!


