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The second part of the fundamental theorem of calculus is my favorite. | 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], | 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) | + | \begin{equation}f(x)=F'(x)\end{equation} |
then | then | ||
<math>\int_a^b f(x) dx</math>=F(b)-F(a) | <math>\int_a^b f(x) dx</math>=F(b)-F(a) | ||
Revision as of 10:21, 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], \begin{equation}f(x)=F'(x)\end{equation} then $ \int_a^b f(x) dx $=F(b)-F(a)
