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Bipolarity

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The proof my book gives for the 2nd part of the FTC is a little hard for me to understand, but I was wondering if this particular proof (which is not from my book) is valid. I did the proof myself, I'm just wondering if it's valid.

[tex] \frac{d}{dx}\int^{x}_{0}f(t) \ dt = f(x) [/tex]

So suppose that the antiderivative of f(t) is F(t).

Then

[tex] \frac{d}{dx}\int^{x}_{0}f(t) \ dt = \frac{d}{dx}(F(x)-F(0)) = F'(x) = f(x) [/tex]

Is this a valid proof? IF not, where am I wrong?

Thanks for your time.

BiP

[tex] \frac{d}{dx}\int^{x}_{0}f(t) \ dt = f(x) [/tex]

So suppose that the antiderivative of f(t) is F(t).

Then

[tex] \frac{d}{dx}\int^{x}_{0}f(t) \ dt = \frac{d}{dx}(F(x)-F(0)) = F'(x) = f(x) [/tex]

Is this a valid proof? IF not, where am I wrong?

Thanks for your time.

BiP

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