integration of derivative problem

Aminul

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integration of derivative problem

please help me to solve this problem.If ʃ(dx/dt)dt=x then how to calculate ʃ(dx/dt)^2dt or ʃ(dx/dt)* (dx/dt)dt . how to get intigration of square of velocity.thanks
 
integration of derivative problem

please help me to solve this problem.

If ʃ(dx/dt)dt=x then how to calculate ʃ(dx/dt)^2dt or ʃ(dx/dt)* (dx/dt)dt .

\(\displaystyle \displaystyle{\int \frac{dx}{dt}dt} = x\) \(\displaystyle + C\) ........ That constant of integration is very important

how to get intigration of square of velocity.thanks

Please post the EXACT problem along with your attempts (even if you think those were incorrect) with it.
 
\(\displaystyle \int \frac{dx}{dt}dt= x+ C\) for x any differentiable function of t. That does not help at all in integrating \(\displaystyle \left(\frac{dx}{dt}\right)^2\).
 
\(\displaystyle \int \frac{dx}{dt}dt= x+ C\) for x any differentiable function of t. That does not help at all in integrating \(\displaystyle \left(\frac{dx}{dt}\right)^2\).

\(\displaystyle \int \frac{dx}{dt}dt= x\) is incorrect for x any differentiable function of t (except when C = 0 has been proven) - whether or not you want to calculate\(\displaystyle \left(\frac{dx}{dt}\right)^2\)

My point was that if the poster is not careful in the first few steps, s/he does not stand a chance to solve the problem correctly.
 
\(\displaystyle \int \frac{dx}{dt}dt= x\) is incorrect for x any differentiable function of t (except when C = 0 has been proven) - whether or not you want to calculate\(\displaystyle \left(\frac{dx}{dt}\right)^2\)

My point was that if the poster is not careful in the first few steps, s/he does not stand a chance to solve the problem correctly.


thank you for your reply.lets say c=0,then how to solve it.I just couldn't.
 
thank you for your reply.lets say c=0,then how to solve it.I just couldn't.

Please post the EXACT problem along with your attempts (even if you think those were incorrect) with it.
 
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