- #1

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## Homework Statement

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

Then F'(x) = f(x)

what is f'(x)? is this equivalent to f(t)?

Thanks for your help

M

- Thread starter michonamona
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- #1

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

Then F'(x) = f(x)

what is f'(x)? is this equivalent to f(t)?

Thanks for your help

M

- #2

Dick

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- #3

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Thanks for the reply.

so f '(x) IS indeed f(t)? the very same f(t) in F(x)?

so f '(x) IS indeed f(t)? the very same f(t) in F(x)?

- #4

Dick

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No. F'(x) is f(x). But, yes, the derivative of the integral is the function you are integrating, isn't that what the fundamental theorem of calculus is all about?Thanks for the reply.

so f '(x) IS indeed f(t)? the very same f(t) in F(x)?

- #5

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so can we write

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

- #6

Mark44

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For example, if F(x) = x

- #7

Dick

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How can f'(x) be the same as f(t)? They don't even involve the same variable.

so can we write

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

- #8

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I appreciate all of your help

M

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