Aug 6th, 2022

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in this video I want to talk about force and work but in the sense of integration so in a very simplified definition of work is Force Times distance its not you know going to your nine-to-five job thats not what were talking about work here in the physical sense work has a quantitative and measurable value so a really simple example would be well if you applied 100 Newtons of force to a block make this block and you pushed it with a hundred Newtons of force for lets just say I dont know two meters well then the amount of work you would have done is a hundred times 2 or 200 and thats simply at work is just force times the distance apply but it gets a little more complicated if youre not just pushing things in straight lines so this is kind of where the integrals come in and here is your formula for how you might solve a work problem in calculus and as the work is the definite integral from A to B of your force function DX so the integral from A to B is kind of like the distanc

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A quantity representing the sum of the kinetic and the potential energy of a mechanical system at a certain moment in time.

So work equals the integral of kx dx, integrated from the initial displacement, 0, to the final displacement, xf. The integral of kx is (kx)^2. And using the values of the limits, that comes out as W = (kxf)^2. So thats our equation for the work done in this process.

Enter the integral in Mathway editor to be evaluated. The Definite Integral Calculator finds solutions to integrals with definite bounds.

1:16 4:08 And as the work is the definite integral from A to B of your force. Function DX so the integral fromMoreAnd as the work is the definite integral from A to B of your force. Function DX so the integral from A to B is kind of like the distance. And obviously the force function is your force.

Because the net force on a particle is equal to its mass times the derivative of its velocity, the integral for the net work done on the particle is equal to the change in the particles kinetic energy. This is the work-energy theorem.

The work done by a constant force of magnitude F on a point that moves a displacement d in the direction of the force is the product: W=Fd. Integration approach can be used both to calculate work done by a variable force and work done by a constant force.

Wolfram|Alpha is a great tool for calculating antiderivatives and definite integrals, double and triple integrals, and improper integrals.

0:04 3:15 CPM Calculus 5-96 - Integration without a calculator (SS) - YouTube YouTube Start of suggested clip End of suggested clip Which what you do is just 3u 1/3 plus 1 over 1/3 plus 1 and you do the boundaries. From 1 to 8. AndMoreWhich what you do is just 3u 1/3 plus 1 over 1/3 plus 1 and you do the boundaries. From 1 to 8. And this would simplify to 9/4 you to the 4/3. And the boundaries of 1 to 8.

To express this concept mathematically, the work W is equal to the force f times the distance d, or W = fd. If the force is being exerted at an angle to the displacement, the work done is W = fd cos .

It states that the integral of the force with respect to time is equal to the change in momentum of the object.

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