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Comprehensive Review of Dot Products and Integration Techniques

This review covers the definition of work, examples of dot products, and methods for calculating a dot product between vectors. It includes explanations on integration, both indefinite and definite, with practical examples demonstrated. Explore the concepts of work, force, and distance with clear illustrations and calculations.

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Comprehensive Review of Dot Products and Integration Techniques

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  1. Review of Dot Products Review of Integration Definition of Work Examples of Work

  2. A B How to calculate a dot product A dot product is the multiplication of two vectors to form a scalar. There are two ways to calculate the dot product. where θ is the angle between A and B Component of A along B θ

  3. 4m 10m Examples of Dot Products 110o

  4. Indefinite Integrals

  5. Definite Integrals

  6. dr F Definition of Work Work is defined as the amount of force acting over a distance. The unit of work is either Joules (J) or electron-volts (eV)

  7. y Δw Δh1 x Δh2 Example of Work The following is an example of the work done by gravity on a mass. m

  8. F (N) 1 A1 0 X (m) -1 A2 1 2 0 Example of Work This is an example using the the fact that integrals are areas under a curve.

  9. This is the last slide. Click the back button on your browser to return to the Ebook.

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