Woocommerce update checkout ajax

Solution:1

This works:

jQuery(document.body).trigger("update_checkout");

Solution:2

Try this one:

jQuery('body').trigger('update_checkout');

You can not use dollar sign $ to call jQuery in wordpress, instead you must use the string jQuery

Have a look at tip 5 in this web page: 5 Tips for using jquery with wordpress:

It is important to know that the version of jQuery that comes with WordPress automatically calls the jQuery.noConflict(); function, which gives control of the $ variable back to whichever library first implemented it. If you are loading a different copy of jQuery, you’ll need to manually call jQuery.noConflict();, if necessary, from one of your JavaScript files.