What is the integral of (dy/dt)^2 ?

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The integral of (dy/dt)^2 with respect to time requires additional information about the function y(t) to be solved completely. Integration by parts can be applied, resulting in the expression y(dy/dt) minus the integral of y multiplied by the second derivative of y with respect to time. This manipulation highlights the complexity of the integral, emphasizing the need for specific details about the function involved. Without such information, a definitive answer cannot be provided. Understanding these nuances is crucial for solving integrals in calculus.
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What is the integral of (dy/dt)^2 ??

As the title reads, I was hoping someone knew what the integral with respect to time of [dy/dt]^2 was.

To clarify, I am looking for: the integral with respect to time of the (time derivative of y)^squared

sorry, can't figure out how to get it to display math characters

if S is the integral sign --> need: S{(dy/dt)^2}dt
 
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To effect that integration more information is needed.
 


There are, however, some manipulations you can do; integration by parts gives y dy/dt - ∫y d2y/dt2 dt.
 

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