Dear Prof.，
I am deeply sorry to inform you that I did not manage to complete the task you designated last week，due to a sudden illness falling upon me these days. For the last week， I have been in a hospital with a continuous fever，which has prevented me any activity.
To make up my fault，could you please ext my deadline to next Friday？If so，I promise I will finish the task and s my report to you via email.
I do apologize again for any inconvenience it might bring to you，and hope you could accept my apology.
Sincerely yours,