Even/Odd Functions 5.5.

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Presentation transcript:

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

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!

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

Partition into subintervals: 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