https://youtu.be/YO0M0w12URo

In this video I go over 2 examples on determining the amount of work or energy required in performing an action. In this video first example the force is constant, which is the force of gravity acting on a book. In the second example the force is variable and thus the amount of Work is calculated by using integrals as the summation of the area of under the force function.

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# Integrals and Work: Examples Part 1

![Integrals and Work Example 1.jpeg](https://cdn.steemitimages.com/DQmTZ5TKDUp5X9ZPJQTzqmppTKatG84axvM8Mx5DKja9x2g/Integrals%20and%20Work%20Example%201.jpeg)

## Example 1: When the force is constant

(a) How much work is done in lifting a 1.2 kg book off the floor to put it on a desk that is 0.7 m high? Use the fact that the acceleration due to gravity is g = 9.8 m/s<sup>2</sup>.

**Solution:**

![](https://cdn.steemitimages.com/DQmXgR5Q2JrDA1b74mKKq7JfBW8ECgMLAFVbAdq2qt9xUkP/image.png)

(b) How much work is done in lifting a 20-lb weight 6 ft off the ground?

**Solution:**

![](https://cdn.steemitimages.com/DQmakDxDGwtVQNQXT25qm514FRT5RSozU5dguN3JUSs6g9C/image.png)

## Example 2: When the force is variable

When a particle is located a distance x feet from the origin, a force of x<sup>2</sup> + 2x pounds acts on it. How much work is done in moving it from x = 1 to x = 3?

**Solution:**

![](https://cdn.steemitimages.com/DQmSVtZLr8Gkz1FGbfdcZLEBn9wRYR22GNUNcnPDRnHcxLC/image.png)