Depends on which model dell.

8GB Kit (4GBx2)  
DDR3 PC3-10600 • CL=9 • Unbuffered • NON-ECC • DDR3-1333 • 1.5V • 512Meg x 64 •   •  Part #: CT1164531

http://www.crucial.com/upgrade/Dell-memory/Studio/Studio+XPS+8100-upgrades.html

http://www.frys.com/product/7275403?site=sr:SEARCH:MAIN_RSLT_PG

Model is Studio XPS 8100 DT bought in Jan 2010.

Thank you very much, Speedstep.

So, based on the diagnostic result 'memory - integrity test failed' do you think buying and installing these modules will solve my problem? 

Take out all ram and try 1 stick at a time.

If one or more work then I would say yes the ram needs replacement.

If all ram tests bad you may have power supply or other issue.