I need to enlarge the opening for a new cooktop in my corian counter by 1/2 inch. I've been told that I can do this with my jigsaw and a wood cutting reverse blade after taping the area to be cut. Is this correct? If not, how would I do this? I would prefer to use my jigsaw rather then a router because of my lack of experience with the router.

Jack,

This very question was answered 2 weeks ago.

https://www.askmehelpdesk.com/interior-home-improvement/how-do-cut-existing-corian-countertop-233840.html?highlight=corian

Pay particular attention to Jim Heaphy's posts.

Jack, you can use a jigsaw, but be sure to sand ALL the chipped edges smooth. If not, the benchtop will crack from a chip. A router will do a better jog as it doesn't chip. You can clamp a template (from craftwood or chipboard) to the benchtop, SECURELY and use the router to cut it to the right size.
Hold the router securely, with both hands, it will only cut one way, that is, in one direction. Determine the direction before laying into it! If it's a good size router, then you shouldn't have any problem, as long as you go in the right direction! All corners should also be rounded to prevent cracking, i.e. use a 7/8" speedbore(if you use a router, the corner will be rounded anyway). You should also use a heat reflective tape around the cut-out to prevent cracking from heat. Cheers. :)

The best tool for this task is probably a laminate trimmer. A laminate trimmer is just a small router built to be used in the confined area of trimming counter top laminate.

Routers and the laminate trimmer are always used with some kind of guide. They are never used free hand. You cannot control a router buy just holding it. A jig saw cuts on the up stroke. The cutting action of the blade holds the saw down on the surface. I don't know of any advantage of reversing the blade and doing so would only make the cutting action of the blade push the saw up and off the surface, making control more difficult. The person that advocated that theory probably did so thinking that the smooth edge would be on the top surface. That might be true if you were cutting a thin piece of plywood. The teeth of the blade exiting the wood does leave some torn wood fibers. If you can, you cut thin plywood with a jig saw from the back side. Unlike plywood Corian has no fibers. The amount of chipping of a fine tooth jig saw blade should not be a concern.

You stated that you have to enlarge the cut out by 1/2". If you attempt to do this evenly you will be trying remove 1/4" from each side. Your jig saw blade will probably be too flexible to cut that small amount. That is about the correct amount to remove with a router or laminate trimmer. With the laminate trimmer you probably should remove 1/8" and make two passes. The only difference in the router and the laminate trimmer is that the trimmer has less power but will let you get closer to the back splash. Neither will let you cut flush with the back splash. There is an accessory for the trimmer that will let you cut flush.

You would glue a straight edge to the counter top with hot melt glue as a guide. You always cut against the rotation of the bit. Therefore, you cut in one direction when the material is on one side of the bit and the other direction when the material is on the other side. That means that you will cut front to back on one side and back to front on the other. There is very little skill involved. The guide controls the cut and the rotation of the bit naturally keeps the router against the guide.

Corian expands and contracts with changes in temperature. The aluminum foil tape is to prevent binding between the sharp metal edge of the under side of the appliance and the surface of the Corian. It is not for heat reflection or conduction purposes.

Actually an "all purpose" blade is recommended in a reciprocating saw of any size (including Jig). This is because a fine tooth blade will fill too quickly causing heat buildup during cutting. I also recommend to any novice that you never cut faster than 30 inches per minute. Practice with a yardstick, I know it seems like the sun is setting in the west. This will keep you from forcing your tool, bending the blade and will keep the gullets of the tool bit or blade clear. Keeping the gullets clear will reduce the fine dust as well as reduce heat buildup.

Regardless of the tool used it is still necessary to sand the edges smooth to eliminate any stress riser effect. The Cooktop should never be in contact with the edge of the Corian hole (conductive heat) and the tape is to disipate the localized radiant and convective heat at the edge. Constant heating and cooling cycles turn granite mountains into seashore. This can also effect Corian over time and therefore must be mitigated as much as possible.