Although you're 40 weeks' gestation and apparently have not had signs of labor beginning, there should be no immediate need to induce your labor unless there is a medical problem or concern (for example, gestational diabetes, or signs of distress in your baby). The "normal" range for labor to begin is between 38 and 42 weeks' gestation. I would ask your physician why he or she wants to induce you. If you and your baby are both fine, I'd suggest waiting a little longer for Mother Nature to get things going naturally.
Induced labors are often more difficult to deal with, requiring you to need medication or an epidural anesthetic much earlier in your labor than if the induction drug Pitocin was not being used. When anesthesia is given early in labor, you're confined to bed, there is the possibility that labor will not progress as well, and a Cesarean delivery may be the result. It's also not wise to have an induction before your cervix has begun to show signs of readiness for labor, such as ripening (softening), effacement (thinning), and beginning dilation. Staying active and walking each day won't necessarily start your labor, but are good for your general well-being. Old-fashioned remedies that our grandmothers used to start labor, such as castor oil or enemas, are not usually effective, either.
If labor has not begun by 42 weeks' gestation, discuss induction with your physician. After that time induction may be wise, because the placenta begins to show signs of aging beyond 42 weeks, and the baby needs to be born. So take a deep breath, be patient, and within another week or so your body will probably decide it's time for labor to begin.