Q:

How do I display equations in TraditionalForm in Mathematica?

I am looking to use Mathematica to print equations in TraditionalForm. 
While I have been successful for some simple ones, I have not for the 2 below.

A:

The standard way to integrate over a region in MMA is:
Integrate[Boole[x^2 + y^2 < r^2] \[Phi][x,y], {x, -r, r}, {y, -r, r}]

MMA doesn't have a TraditionalForm for that, so you have to make one yourself:
1) Type Integrate[\[Phi][x,y],x,y].
2) Change to Traditional Form (using  ctrl shift-T)
3) Select the second integral. Make a subscript using ctrl-_ and x^2+y^2<=r^2 in 2D form  

As to the second one, as NormalDistribution hasn't got a TraditionalForm definition you have to type it yourself either following Yoda's recipe or make a definition yourself:
Unprotect[NormalDistribution];
NormalDistribution /: 
   Format[NormalDistribution[m_, s_],TraditionalForm] := \[ScriptCapitalN] [m, s]
Protect[NormalDistribution];

or, to make it go both ways, use the Notation package.

A:

I think you're trying to enter these expressions in your text/notes/presentations in mma. Here's an example
"\!\(\*SubscriptBox[\(\[Integral]\), \(\\\ \)]\)\!\(\*SubscriptBox[\(\
\[Integral]\), \(\*SuperscriptBox[\(x\), \(2\)] + \
\*SuperscriptBox[\(y\), \(2\)] \[LessEqual] \*SuperscriptBox[\(r\), \
\(2\)]\)]\)\[CapitalPhi](x,y)\[DifferentialD]x\[DifferentialD]y" // \
TraditionalForm

"\!\(\*SubscriptBox[\(X\), \
\(1\)]\)~\[ScriptCapitalN](\!\(\*SubscriptBox[\(\[Mu]\), \
\(1\)]\),\!\(\*SuperscriptBox[SubscriptBox[\(\[Sigma]\), \(1\)], \
\(2\)]\))" // TraditionalForm

The keystrokes for this one are:
X, Ctrl-1, →, ~, EscscNEsc, (, EscmEsc, Ctrl-1, →,
    EscsEsc, Ctrl-1, →, Ctrl62, →, )
I'll leave the other one to you.

