How Do You Integrate (dx/dt) dx in Physics Problems?

[danunicamp]

Good Night,

Can someone please tell me how to do: ∫ b (dx/dt) ⋅ dx ?

Like in the work done by a force which is proportional to the velocity (like drag). I tried to change dx to v dt but couldn´t go much further.

Thank you in advance.

 

[andrewkirk]

If you write $v=\frac{dx}{dt}$ then you have $dx=v\,dt$ and you can write your equation as $\int b\,v^2 dt$.

 

[Orodruin]

Note that it is sometimes easier to express $dx/dt$ as a function of $x$ rather than $t$. In these cases, you can simply integrate that function. You really cannot get any further without having a specific integral to do. Note that such a problem should be posted in the homework forums with the template properly filled in, including your own attempt and the full problem statement.

 

[danunicamp]

If you write $v=\frac{dx}{dt}$ then you have $dx=v\,dt$ and you can write your equation as $\int b\,v^2 dt$.

Thank you very much