The first fundamental theorem of calculus

  • #1
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Say I have the statement ##\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 ##F(x) = \int_{a}^{x}f(t)dt##. How does the later apply to the former if the former is an antiderivative?
 

Answers and Replies

  • #2
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BUT Y= F(X)
SO, dy/dx=f(x)
la segunda es integral definida
 
  • #3
1,007
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Say I have the statement ##\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 ##F(x) = \int_{a}^{x}f(t)dt##. How does the later apply to the former if the former is an antiderivative?
Do you know the Leibniz rule?
 

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