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Study23 Group Title

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)??????

  • one year ago
  • one year ago

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  1. satellite73 Group Title
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    it means, in english, that "the derivative of the integral is the integrand"

    • one year ago
  2. Study23 Group Title
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    I'm confused about the d/dx part in particular...

    • one year ago
  3. satellite73 Group Title
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    that is, if \[F(x)=\int_a^xf(t)dt\] then \[F'(x)=f(x)\]

    • one year ago
  4. satellite73 Group Title
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    notice that \[F(x)=\int_a^xf(t)dt\] is a function of the variable \(x\) and not of \(t\)

    • one year ago
  5. satellite73 Group Title
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    for example, if \[F(x)=\int_0^x\sin(t)dt\] then \[F'(x)=\sin(x)\]

    • one year ago
  6. Study23 Group Title
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    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?

    • one year ago
  7. satellite73 Group Title
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    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

    • one year ago
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