- #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!

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- 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

- 761

- 13

I think partial integration can work.

- #3

- 70

- 0

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

- 761

- 13

Wait a second is x(t) explicitly known?

- #5

- 6

- 0

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

Thanks!

- #6

HallsofIvy

Science Advisor

Homework Helper

- 41,847

- 969

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

even has an elementary anti-derivative.

- #7

- 761

- 13

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

- 6

- 0

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.

Share: