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5.2 Cont.

5.2 Cont. Signed Area, Displacement, Accumulation Finding the Value of Integrals from our knowledge of functions. Partner Problem. The Relationship of the Integral to Area. Signed Area.

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5.2 Cont.

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  1. 5.2 Cont. Signed Area, Displacement, Accumulation Finding the Value of Integrals from our knowledge of functions

  2. Partner Problem

  3. The Relationship of the Integral to Area

  4. Signed Area Consider the graph to the left. If this is the graph of the velocity of an object moving along a horizontal line over time, what does the area between the graph and the t-axis mean? The integral is defined as the “signed” area between a graph and the x-axis. Area above the x-axis is defined as positively signed area. What does this area represent in terms of the movement of the particle? Area below the x-axis is defined as negatively signed area. What does this area represent in terms of the movement of the particle?

  5. More on Area This does not mean that area means anything different than it did in Geometry: The Integral in relation to Geometric area:

  6. Exploration

  7. More practice with signed areas:

  8. Using NINT (or on your calculator, fnInt) Method 1: press Math 9 and enter the following parameters: Method 2: graph the function and use 2nd-Calc 7

  9. Assignments: • 5.2B: p. 273: 34; p. 282: 2,6,16,26,29, 31,33,41,47-49

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