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Even/Odd Functions 5.5
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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
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ODD EVEN
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Even Function
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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!
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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
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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
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