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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
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 Originally Posted by Mr Davis 97 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?
It $\displaystyle doesn't$! What you should have is that $\displaystyle \int \frac{dy}{dx} dx= y+ C$ where "C" can be any constant. Tags calculus, fundamental, theorem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Mr Davis 97 Calculus 6 June 5th, 2014 02:29 PM MadSoulz Real Analysis 2 April 15th, 2014 03:19 PM Aurica Calculus 1 June 14th, 2009 08:04 AM Aurica Calculus 1 June 10th, 2009 05:39 PM mrguitar Calculus 3 December 9th, 2007 01:22 PM

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