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April 16th, 2015, 02:25 PM  #1 
Senior Member Joined: Feb 2014 From: Louisiana Posts: 156 Thanks: 6 Math Focus: algebra and the calculus  The first fundamental theorem of calculus
Say I have the statement $\displaystyle \int \frac{\mathrm{d} y}{\mathrm{d} x}\mathrm{d}x = y$ How does the fundamental theorem of calculus make this necessarily true? When I see the formal statement of the theorem, it is usually in terms of a definite integral such as $\displaystyle F(x) = \int_{a}^{x}f(t)dt$. How does the later apply to the former if the former is an antiderivative and not a definite integral?

April 16th, 2015, 04:06 PM  #2  
Math Team Joined: Jan 2015 From: Alabama Posts: 2,731 Thanks: 705  Quote:
 

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