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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The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus

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