| (2 intermediate revisions by the same user not shown) | |||
| Line 3: | Line 3: | ||
f(x)=F'(x) | f(x)=F'(x) | ||
then | then | ||
| − | <math> | + | <math>\int_a^b f(x) dx</math>=F(b)-F(a) |
Latest revision as of 10:22, 2 September 2008
The second part of the fundamental theorem of calculus is my favorite. Let f be a continuous real-valued function defined on a closed interval [a,b]. Let F be an antiderivative of f, that is one of the indefinitely many functions such that, for all x in [a,b], f(x)=F'(x) then $ \int_a^b f(x) dx $=F(b)-F(a)
