- #1

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I am trying to figure out how to integrate this, I know it must be simple but I am not sure how to do it.

[tex]\int(\frac{dx}{dt})^{2}dt[/tex]

Thanks a lot!

- Thread starter gilgtc
- Start date

- #1

- 6

- 0

I am trying to figure out how to integrate this, I know it must be simple but I am not sure how to do it.

[tex]\int(\frac{dx}{dt})^{2}dt[/tex]

Thanks a lot!

- #2

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I think partial integration can work.

- #3

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You just need x defined in terms of t

x = x(t)

then you can differentiate with respect to t,

then you square dx/dt

then you integrate that across t from t1 to t2

right?

x = x(t)

then you can differentiate with respect to t,

then you square dx/dt

then you integrate that across t from t1 to t2

right?

Last edited:

- #4

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Wait a second is x(t) explicitly known?

- #5

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Any other ideas? What do you mean by partial integration dirk_mec1?

Thanks!

- #6

HallsofIvy

Science Advisor

Homework Helper

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[tex]\right(\frac{dx}{dt}\)^2[/tex]

even has an elementary anti-derivative.

- #7

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I dont think you can just integrate [tex] \int (f'(x))^2 \mbox{d}x[/tex], right? The integration by parts(thanks hallsofIvy ) however gives:

[tex] x (x'(t))^2 - \int x \cdot 2x' \cdot x''\ \mbox{d}t [/tex]

[tex] x (x'(t))^2 - \int x \cdot 2x' \cdot x''\ \mbox{d}t [/tex]

Last edited:

- #8

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I thought that there was an easy equivalence like:

[tex]\int(dx/dt)dt = x[/tex]

I guess not! thanks for your help in any case.

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