The end of the positive battery cable broke where it connects to the battery. How do I replace it?

The best way is to buy a factory replacement cable at a dealer. This could be expensive or impossible if it is over 10 years old so the next best thing is to buy a generic positive battery cable at an auto parts store. You most likely drive by many such stores every day. take your old cable in and see if they have one hanging on the wall about that length, other wise you will have to cut one to right length and put on a new terminal yourself, and that connection is where the corrosion starts to build anew. they will have a clear coat paint you spray over the cable connections, it will slow down the corrosion but not stop it. with one end of the cable already disconnected you can take the other end off with a wrench, it connects to the starter. the best way to install your new cable is to first take off the other negative ground cable at the battery terminal. then install your positive cable hooking one end to the starter and the other end to the battery, then hook the negative ground cable back up. this methoad prevents sparking

Go to the auto parts store and purchase a replacement clamp. Expect to pay less than $6.00 for the clamp. Cut the wire back to a clean place, strip about 1/2 inch insulation away and insert it into the clamp and tighten.

I trust this answers your question satisfactorily.