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5.4 Indefinite Integrals

This lesson focuses on the concept of indefinite integrals as antiderivatives, exploring key examples including the calculation of displacement and distance traveled by a particle from its velocity function. We discuss the Total Change Theorem, illustrating how the integral of a rate of change corresponds to total change. An example demonstrates evaluating the displacement over a time interval, and additional examples help consolidate understanding of these concepts. Homework problems are provided for further practice to deepen learning.

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5.4 Indefinite Integrals

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  1. 5.4 Indefinite Integrals

  2. Indefinite Integral = Antiderivative

  3. Ex 1: Evaluate

  4. Ex 2: Evaluate

  5. The Total Change Theorem: The integral of a rate of change is the total change.

  6. Ex 3: A particle moves along a line so that its velocity at time x is (m/sec). a) Find the displacement from x = 0 to 2 seconds.

  7. Displacement: Total Change in Position Distance:

  8. Ex 3: A particle moves along a line so that its velocity at time x is (m/sec). b) Find the distance traveled during this time period.

  9. HW: 5.4 pg. 407# 1 – 41 EOO, 45, 53, 55

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