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December 8th, 2012, 12:25 AM   #1
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What are the similarities of differential and integral calcu

What are the similarities of differential and integral calculus?
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December 8th, 2012, 08:23 AM   #2
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Re: What are the similarities of differential and integral c

Its not really a matter of "similarities", the two are "inverse" to one another.
The two parts of the "Fundamental Theorem of Calculus":

If f(x)= dF/dx, then ..

If F(x)= \int_a^x f(x)dx, then dF/x= f(x).

One important difference between differentiation and integration is that we have a specific definition for differentiation: but integration is only defined "indirectly": is a function whose derivative is f(x). That means that integrating, often, is a matter of searching for an anti-derivative rather than "computing" it directly.
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