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Functions Defined by Integrals

Part 4: A Third Example

  1. In your worksheet, define

    third example

    Graph this function.

  2. Define the corresponding function F(x), and graph it. Explain why it has the form it has. Ask your helper application to give you a simplified symbolic formula for F(x). What -- if anything -- do you think this formula means?

  3. Differentiate F(x), and confirm that the result is f(x).

  4. Define g(x) as the appropriate integral of f '. Graph g, and compare the graph with that of f. Confirm that g(x) = f(x) - f(0).

  5. (optional) Explain why F is the solution of the initial value problem

    IVP

  6. (optional) Explain why g is the solution of the initial value problem

    IVP

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