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
\(\displaystyle \int \frac{dx}{dt}dt= x+ C\) 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.
thank you for your reply.lets say c=0,then how to solve it.I just couldn't.