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

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In summary, the integral of (dy/dt)^2 is the process of finding the area under the curve of the function (dy/dt)^2 with respect to the variable t. It is calculated using integration techniques and has various applications in mathematics and physics. It can have a negative value and differs from the integral of dy/dt in terms of the concept it represents and the resulting function.
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ELEN_guy
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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.
 
  • #3


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

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

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

The integral of (dy/dt)^2 is the process of finding the area under the curve of the function (dy/dt)^2 with respect to the variable t. It represents the accumulation of the squared rate of change over a certain interval.

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

The integral of (dy/dt)^2 is calculated by using integration techniques such as substitution, integration by parts, or using specific integral rules, depending on the form of the function (dy/dt)^2. It is important to note that the integral of (dy/dt)^2 is not always easy to calculate and may require advanced techniques.

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

The integral of (dy/dt)^2 has various applications in mathematics and physics, such as in solving differential equations, calculating work and energy, and determining the velocity and acceleration of an object. It also has connections to the concept of the area under a curve and the fundamental theorem of calculus.

Can the integral of (dy/dt)^2 have a negative value?

Yes, the integral of (dy/dt)^2 can have a negative value. This means that the area under the curve of (dy/dt)^2 can be below the x-axis. This can occur if the function (dy/dt)^2 is negative or if the area below the curve is subtracted from the area above the curve.

How does the integral of (dy/dt)^2 differ from the integral of dy/dt?

The integral of (dy/dt)^2 and the integral of dy/dt represent different concepts. The integral of (dy/dt)^2 represents the accumulation of the squared rate of change, while the integral of dy/dt represents the accumulation of the rate of change itself. Additionally, the integral of (dy/dt)^2 results in a function of t, while the integral of dy/dt results in a function of y.

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