You can't. Printing requires you to write a class that implements the Printable interface where you would render the graphic for the print. What you can do is write a class (anonymous is fine as well) which is given the text of the JTextArea that then creates the graphics using the graphic's drawString() method.
Once you have that, you use pj.setPrintable(myPrintableObject); then issue pj.print().
header('HTTP/1.1 420 Enhance Your Calm');