engage vs involve

engage

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

  • To enter into conflict with (an enemy). 

  • To come into gear with. 

  • 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 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. 

involve

verb
  • To cause or engage (someone or something) to participate or to become connected or implicated. 

  • To take in; to gather in; to mingle, blend or merge. 

  • To comprise or include; to have as a related part. 

  • To complicate or make intricate. 

  • To envelop, enfold, entangle. 

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