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8.1 accumulation and net change pearson
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Uploaded: 4 years ago
Category: Calculus
Type: Lecture Notes
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Filename: 8.1_accumulation_and_net_change_pearson.pptx
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Page Count: 15
Credit Cost: 2
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Transcript
Section 8.1
Accumulation and
Net Change
Applications of Definite Integral
Chapter 8
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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