Accumulation and Net Change

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Presentation transcript:

Accumulation and Net Change Chapter 8 Applications of Definite Integral Section 8.1 Accumulation and Net Change

Quick Review

Quick Review Solutions

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.

Example Linear Motion Revisited

Example Linear Motion Revisited

Example Linear Motion Revisited

Strategy for Modeling with Integrals

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.

Example Potato Consumption

Example Potato Consumption

Work

Hooke’s Law

Example A Bit of Work

Example A Bit of Work

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