As nouns the difference between study and investigation is that study is (label) a state of mental perplexity or worried thought while investigation is the act of investigating; the process of inquiring into or following up; research; study; inquiry, especially patient or thorough inquiry or examination; as, the investigations of the philosopher and the mathematician; the investigations of the judge, the moralist.

As a verb study is (usually|academic) to revise materials already learned in order to make sure one does not forget them, usually in preparation for an examination.

Source: Wikidiff

I want to explain that as a research methodology. Can you give me an example?

Dear Mohammad

I think the word "investigation" refers to a new thing or method and is more deeper than study.

Dear Mohammad

First thank you for this question, and also,  may thanks for all authors for their explanations;

From point view of science and engineering the word "Investigation" it is used when the research included or specified in  "Experimental Work" and not a theoretical work. Ont he other hand, the word "Study" it is global word and   used to express  all types of research work.

Thank you for your contributions