Please read this great article about what a medical induction can put you at risk for. If anyone tells you medical inductions are risk-free they are lying, and I don't know how else to say it. There are clear advantages for babies who "cook" longer, as this study showed. A baby who is born early has not finished their development yet. Currently, we think it is the baby's own finished development that triggers labor to begin. So your body is not broken if you pass your due date. Your baby is just not ready for the outside world yet. After all, that due date is just a guess of an average. Actual pregnancy length can vary by FIVE WEEKS, as this study on pregnancy length explains.
So, although it's much easier for me to say because I'm not 9 months pregnant I would encourage you to enjoy these last few days of pregnancy knowing that you're doing a good thing for yourself and your baby.