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Even/Odd Functions

Even/Odd Functions. 5.5. RECALL. A function is even if: f(-x) = f(x) Symmetric with y-axis A function is odd if: f(-x) = -f(x) Symmetric with origin. ODD. EVEN. Even Function.

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Even/Odd Functions

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  1. Even/Odd Functions 5.5

  2. RECALL • A function is even if: f(-x) = f(x) • Symmetric with y-axis • A function is odd if: f(-x) = -f(x) • Symmetric with origin

  3. ODD EVEN

  4. Even Function

  5. When we use definite integrals to compute area, we need to be careful to distinguish net area (where area below the x-axis is counted as negative) from the total area. If asked to find area, total area is assumed!

  6. To find area over a given interval • Partition [a,b] with the zeros of f • Integrate f over each subinterval • Add the absolute value of the integrals

  7. Example Find the area of region between the x-axis and in the interval [-1, 2] Partition into subintervals: [-1, 0] and [0, 2] Total Area: 37/12

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