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The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus

We can see from this picture that the Fundamental Theorem of Calculus works. By definition, the derivative of $A(x)$ is equal to $\frac{A(x+h)−A(x)}{h}$ as $h$ tends to zero. By replacing the numerator, $A(x+h)−A(x)$, by $hf(x)$ and dividing by $h$, $f(x)$ is obtained. Taking the limit as $h$ tends to zero completes the proof of the Fundamental Theorem of Calculus.

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    http://upload.wikimedia.org/wikipedia/commons/thumb/e/e6/FTC_geometric.svg/627px-FTC_geometric.svg.png CC BY-SA.

Related Terms

  • antiderivative
  • derivative
  • definite integral
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