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 one year 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)??????
 one year 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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satellite73
 one year ago
Best ResponseYou've already chosen the best response.0it means, in english, that "the derivative of the integral is the integrand"

Study23
 one year ago
Best ResponseYou've already chosen the best response.0I'm confused about the d/dx part in particular...

satellite73
 one year ago
Best ResponseYou've already chosen the best response.0that is, if \[F(x)=\int_a^xf(t)dt\] then \[F'(x)=f(x)\]

satellite73
 one year ago
Best ResponseYou've already chosen the best response.0notice that \[F(x)=\int_a^xf(t)dt\] is a function of the variable \(x\) and not of \(t\)

satellite73
 one year ago
Best ResponseYou've already chosen the best response.0for example, if \[F(x)=\int_0^x\sin(t)dt\] then \[F'(x)=\sin(x)\]

Study23
 one year ago
Best ResponseYou've already chosen the best response.0So 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?

satellite73
 one year ago
Best ResponseYou've already chosen the best response.0the \(\frac{d}{dx}\) 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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