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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 .. 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 antiderivative rather than "computing" it directly. 

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