fundamental theorem of calculus

[computerages]

hello everyone,

 

fundamental theorem of calculus is just one of the smallest parts of calculus so why we make it sound like differential equations (or even more than that)? What is so fundamental about it (if there's something)?

 

also, can someone please explain how do we derive to this theorem.... I am just reluctant to accept something I don't really understand/know?

 

thx

[D H]

It is fundamental because it relates integration and differentiation. What could be more fundamental (in realm of the calculus) than a theorem that relates the two core concepts of the calculus?

 

A proof is here. Google is your friend.

[Dave]

Additionally, it's not very obvious. One wouldn't immediately think that there is a relation between the area under a curve and the tangent line to it - it's really quite remarkable that there are such relations.

[alex]

i always thought it was the biggest part of calculus. definitley the most fundamental.

 

aptly named in my opinion.