I am 37weeks preg, my doctor said baby's heart beat is rapid and she have to do an induction to labor in able to save the baby. Should I let her?

Must trust your md. This is the kind of question that can really be answered in person with full knowledge of patient and clinical exam. You must trust your doctor in these circumstances or get a second opinion in person and not in this forum. Good luck.
Your kidding right ? If your babies heart is beating at a fast rate without any of the stresses of labor, it is telling you/your doc, that it is in distress.Many issues can cause this from a cord with a knot in it to one wrapped around babies neck or some other weakness in baby.This also means there is good reason to get baby out soon & if induction raises the heart rate too much a surgical delivery would be needed.