engage vs intrigue

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. 

intrigue

verb
  • To arouse the interest of; to fascinate. 

  • To have clandestine or illicit intercourse. 

  • To conceive or carry out a secret plan intended to harm; to form a plot or scheme. 

  • To fill with artifice and duplicity; to complicate. 

noun
  • A complicated or clandestine plot or scheme intended to effect some purpose by secret artifice; conspiracy; stratagem. 

  • The plot of a play, poem or romance; the series of complications in which a writer involves their imaginary characters. 

  • Clandestine intercourse between persons; illicit intimacy; a liaison or affair. 

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