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you can utilize a relative date filter to do this. Check out http://onlinehelp.tableau.com/v10.0/pro/desktop/en-us/help.htm#qs_relative_dates.html?Highlight=relative date filter for more info.
I hope this helps.
Hi shiva kumar
Tableau currently does not support the feature of setting default value in Quick Filter. But this feature is still under consideration and you can vote up for the same in the link given below
Alternatively you can also use the concept of relative date filter as suggested by Patrick A Van Der Hyde
You can also look into the blog written by Joshua Milligan on how to dynamically set default values for quick filters In addition you also look into this