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Fundamental theorem of calculus (view source)
Revision as of 18:25, December 30, 2008
, 18:25, December 30, 2008→The Theorem: clarified what the Fundamental Theorem of Calculus says in words
<br />It follows that:
<br />It follows that:
<br /><math>F'(x) = f(x)</math>
<br /><math>F'(x) = f(x)</math>
<br />The first part states that if a function <math>F</math> is the antiderivative of a function <math>f</math>, then the derivative of <math>F</math> is <math>f</math>. In other words, antiderivative and derivative are opposite functions.
===Part 2===
===Part 2===
<br />Then:
<br />Then:
<br /><math>\int_a^b f(x) = F(b) - F(a)</math>
<br /><math>\int_a^b f(x) = F(b) - F(a)</math>
<br />The second part begins with what we know from part 1.
<br />It then states that the definite integral of the function <math>f</math> from <math>a</math> to <math>b</math> is equal to <math>F</math> evaluated at <math>b</math> minus <math>F</math> evaluated at <math>a</math>.
==See also==
==See also==