Endeavor

1. To exert physical or intellectual strength for the attainment of; to use efforts to effect; to strive to achieve or reach; to try; to attempt.
   
To endeavor one's self ,
to exert one's self strenuously to the fulfillment of a duty.

1. To exert one's self; to work for a certain end.
   

Usually with an infinitive; as, to endeavor to outstrip an antagonist. 1913 Webster He had . . . endeavored earnestly to do his duty. Prescott.
n.

1. An exertion of physical or intellectual strength toward the attainment of an object; a systematic or continuous attempt; an effort; a trial.
   
To do one's endeavor ,
to do one's duty; to put forth strenuous efforts to attain an object; -- a phrase derived from the Middle English phrase “to do one's dever” (duty).