- #1

michonamona

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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

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- Thread starter michonamona
- Start date

- #1

michonamona

- 122

- 0

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

Science Advisor

Homework Helper

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- #3

michonamona

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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

Science Advisor

Homework Helper

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Thanks for the reply.

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

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?

- #5

michonamona

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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

Mentor

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For example, if F(x) = x

- #7

Dick

Science Advisor

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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]

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

- #8

michonamona

- 122

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I appreciate all of your help

M

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