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 December 8th, 2012, 12:25 AM #1 Newbie   Joined: Dec 2012 Posts: 1 Thanks: 0 What are the similarities of differential and integral calcu What are the similarities of differential and integral calculus?
 December 8th, 2012, 08:23 AM #2 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 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 $\int_a^b f(x)= F(b)- F(a)$.. 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: $df/dx= \lim_{h\to 0} \frac{f(x+h)- f(x)}{h}$ but integration is only defined "indirectly": $\int f(x)dx$ 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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