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Study23

  • 3 years ago

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)??????

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  1. anonymous
    • 3 years ago
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    it means, in english, that "the derivative of the integral is the integrand"

  2. Study23
    • 3 years ago
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    I'm confused about the d/dx part in particular...

  3. anonymous
    • 3 years ago
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    that is, if \[F(x)=\int_a^xf(t)dt\] then \[F'(x)=f(x)\]

  4. anonymous
    • 3 years ago
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    notice that \[F(x)=\int_a^xf(t)dt\] is a function of the variable \(x\) and not of \(t\)

  5. anonymous
    • 3 years ago
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    for example, if \[F(x)=\int_0^x\sin(t)dt\] then \[F'(x)=\sin(x)\]

  6. Study23
    • 3 years ago
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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?

  7. anonymous
    • 3 years ago
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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

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