busy vs engage

busy

verb
  • To make somebody busy or active; to occupy. 

  • To rush somebody. 

adj
  • Having a lot going on; complicated or intricate. 

  • Officious; meddling. 

  • Engaged in activity or by someone else. 

  • Crowded with business or activities; having a great deal going on. 

noun
  • A police officer. 

engage

verb
  • To engross or hold the attention of; to keep busy or occupied. 

  • To enter into conflict with (an enemy). 

  • To come into gear with. 

  • To enter into (an activity), to participate (construed with in). 

  • To draw into conversation. 

  • To mesh or interlock (of machinery, especially a clutch). 

  • To attract, to please; (archaic) to fascinate or win over (someone). 

  • To guarantee or promise (to do something). 

  • To arrange to employ or use (a worker, a space, etc.). 

  • To bind through legal or moral obligation (to do something, especially to marry) (usually in passive). 

  • To enter into battle. 

How often have the words busy and engage occurred in a corpus of books? (source: Google Ngram Viewer )