Question: Let f(x) be a continuous function with f(x) 0 for a x b. Let R be the region with area A that

Let f(x) be a continuous function with f(x) ≥ 0 for a ≤ x ≤ b. Let R be the region with area A that is bounded by the curve y = f(x), the x axis, and the lines x = a and x = b. Then the centroid (or center) of R is the point (x̅, y̅), where

X 7 - = - 1x A a xf(x) dx and y

In Exercises 65 and 66, find the centroid of the region shown. You may need to use one or more formulas from Table 6.1.

= Life a 2A [f(x)] dx

X 7 - = - 1x A a xf(x) dx and y = Life a 2A [f(x)] dx

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