How long can you go before being induced ?

Anastasia
Today was my 38 week appointment and my cervix is closed up. Idc I figured it would be like that, I'm not physically extremely uncomfortable. My husband asked him at what point would he need to induce me and he said that he wouldn't let me go past 41 weeks regardless of my cervix status. It is funny because I know cervix status is subject to change quickly, but the doctor and the nurse both seemed disappointed that I was still closed.