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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
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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satellite73Best ResponseYou've already chosen the best response.0
it means, in english, that "the derivative of the integral is the integrand"
 one year ago

Study23Best ResponseYou've already chosen the best response.0
I'm confused about the d/dx part in particular...
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
that is, if \[F(x)=\int_a^xf(t)dt\] then \[F'(x)=f(x)\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
notice that \[F(x)=\int_a^xf(t)dt\] is a function of the variable \(x\) and not of \(t\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
for example, if \[F(x)=\int_0^x\sin(t)dt\] then \[F'(x)=\sin(x)\]
 one year ago

Study23Best ResponseYou've already chosen the best response.0
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

satellite73Best ResponseYou've already chosen the best response.0
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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