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Accumulation and Net Change

Accumulation and Net Change. Chapter 8. Applications of Definite Integral. Section 8.1. What you’ll learn about. Displacement as integral of velocity Total distance as integral of absolute value of velocity Modeling accumulation using Riemann sum approximations

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Accumulation and Net Change

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  1. Accumulation andNet Change Chapter 8 Applications of Definite Integral Section 8.1

  2. What you’ll learn about • Displacement as integral of velocity • Total distance as integral of absolute value of velocity • Modeling accumulation using Riemann sum approximations • Interpretation of limits of Riemann sums as definite integrals • Finding net change given graphical and/or tabular representations of rate of change …and why The integral is a tool that can be used to calculate net change and total accumulation.

  3. Example Linear Motion Revisited

  4. Strategy for Modeling with Integrals

  5. Example 2

  6. Consumption over Time The integral is a natural tool to calculate net change and total accumulation of more quantities than just distance and velocity. Integrals can be used to calculate growth, decay, and, as in the next example, consumption. Whenever you want to find the cumulative effect of a varying rate of change, integrate it.

  7. Example Potato Consumption

  8. Example 4

  9. Work

  10. Hooke’s Law

  11. Example A Bit of Work

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