Who was the first to prove the fundamental theorem?

[armolinasf]

Just curious who wrote the first proof of the fundamental theorem of calculus. Thanks.

[mathman]

Try google. The theorem was first proven rigorously by Cauchy.

[HallsofIvy]

There were many people who found different ways of finding tangent lines, and, in particular, the slope of the tangent line (i.e. derivative) before Newton or Leibniz. And finding areas by dividing into smaller and smaller sections goes back to Archimedes. It is the discovery of the "fundamental theorem", that states that these two problems are, in an important sense, "inverse" that make Newton and Leibniz the "creators" of the Calculus. Cauchy may well have been the one to prove the theorem rigorously, using limits (Newton and Leibniz used nebulous appeals to "infinitesmals" rather than limits), but the theorem was "discovered" by Newton and Leibniz.

[phyzguy]

Wikipedia claims that the theorem was known even before Newton and Leibnitz, and was first proved by James Gregory and Isaac Barrow.

http://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus