displace vs engage

displace

verb
  • To supplant, or take the place of something or someone; to substitute. 

  • To move something, or someone, especially to forcibly move people from their homeland. 

  • To put out of place; to disarrange. 

  • To repress. 

  • To have a weight equal to that of the water displaced. 

  • To replace, on account of being superior to or more suitable than that which is being replaced. 

engage

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

  • 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 guarantee or promise (to do something). 

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

  • 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 displace and engage occurred in a corpus of books? (source: Google Ngram Viewer )