anonymous
  • anonymous
Help with Part 1 of the Fundamental Theorem of Calculus?? What does this mean? (d/dx) integral x to a f(t) dt = f(x)??????
Mathematics
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anonymous
  • anonymous
Help with Part 1 of the Fundamental Theorem of Calculus?? What does this mean? (d/dx) integral x to a f(t) dt = f(x)??????
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
it means, in english, that "the derivative of the integral is the integrand"
anonymous
  • anonymous
I'm confused about the d/dx part in particular...
anonymous
  • anonymous
that is, if \[F(x)=\int_a^xf(t)dt\] then \[F'(x)=f(x)\]

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anonymous
  • anonymous
notice that \[F(x)=\int_a^xf(t)dt\] is a function of the variable \(x\) and not of \(t\)
anonymous
  • anonymous
for example, if \[F(x)=\int_0^x\sin(t)dt\] then \[F'(x)=\sin(x)\]
anonymous
  • anonymous
So what does that mean d/dx mean exactly? Does it have todo with the dx dummy variable? Sorry, but that d/dx I throwing me off. Does it mean I have to take the derivative once I find the anti derivative?
anonymous
  • anonymous
the \(\frac{d}{dx}\) notation just means the derivative wrt \(x\) do not be confused by that, it is the same as saying the derivative of the integral is the integrand

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