Does anyone know the proof that definite integral is area of a funtion....

just curious....

:stupid:
Posted on 2003-06-19 14:21:24 by Gandalf
I know, but can't explain this only using text, with my bad english. :grin: :grin: :grin:
Look at the Gauss's definition of the "definite integral". It's a sum of elementary areas, contined in the whole area with borders function and x-axis.
Posted on 2003-06-19 14:45:52 by JohnFound
Err... that's sort of like asking "can you prove that adding two numbers gives their sum?" isn't it?
Posted on 2003-06-19 15:54:51 by Sephiroth3
It is defined as the sum of the partition areas from a to b as the number of partitions approaches infinity. Work it out for two partitions and extrapolate to general solution. :)

http://hyperphysics.phy-astr.gsu.edu/hbase/integ.html
Posted on 2003-06-19 16:14:26 by bitRAKE