# The force applied against a moving object travelling on a linear path is given by #F(x)= sinx + 1 #. How much work would it take to move the object over #x in [ 0, (5pi) / 2 ] #?

I got

To find the complete Work we integrate to get:

We use the Fundamental Theorem of Calculus and get:

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The work done is the integral of the force function over the given interval:

∫[0, 5π/2] (sin(x) + 1) dx = [-cos(x) + x] from 0 to 5π/2 = [-cos(5π/2) + 5π/2] - [-cos(0) + 0] = [0 + 5π/2] - [-1 + 0] = 5π/2 + 1.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- The force applied against a moving object travelling on a linear path is given by #F(x)= 4x + 4#. How much work would it take to move the object over #x in [ 4 , 7] #?
- A spring with a constant of #7 (kg)/(s^2)# is lying on the ground with one end attached to a wall. An object with a mass of #4 kg # and speed of # 2 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?
- An object with a mass of #4 kg# is hanging from an axle with a radius of #5 m#. If the wheel attached to the axle has a radius of #35 m#, how much force is needed to raise the object?
- How can simple machines trade force for distance?
- How much work would it take to push a # 3 kg # weight up a # 13 m # plane that is at an incline of # (5pi) / 12 #?

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