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SgrA*
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How do I perform this integration:
[itex]\int \left (\frac{dy}{dx}\right)^{2} dx[/itex]
Thanks!
[itex]\int \left (\frac{dy}{dx}\right)^{2} dx[/itex]
Thanks!
As posted before, this is not possible in a general way. If you know v(t) or x(t), there could be a solution.but I'm not sure how I'd do it.
There is no reason to assume that an arbitrary integral can be evaluated analytically.SgrA* said:Secondly, why is it that the the integral cannot be evaluated for a general [itex]x(t)[/itex]?
mfb said:There is no reason to assume that an arbitrary integral can be evaluated analytically.
Hi SgrA !SgrA* said:why is it that the the integral cannot be evaluated for a general [itex]x(t)[/itex]?
JJacquelin said:What do you mean by "evaluated" ?
Apparently, you don't understand.SgrA* said:I wanted to evaluate it analytically, but apparently that's not possible.
The formula for the integral of derivative squared is ∫[(d/dx)f(x)]^2 dx, where f(x) is the function being differentiated.
The integral of derivative squared is related to the original function by the Fundamental Theorem of Calculus, which states that the integral of a function's derivative is equal to the original function.
The integral of derivative squared is important because it is used in many applications, such as finding the area under a curve, calculating work and energy, and solving differential equations.
The steps for evaluating the integral of derivative squared are:
Yes, the integral of derivative squared can be negative. This would occur if the function being differentiated has a negative slope over the given interval, resulting in a negative value for the squared derivative.