In this video I go over the more general case of determining the centroid, or center of mass, of a region and this time look at the case where the region is bounded by two curves. In my earlier video I derived the centroid for the case where the region was bounded by the curve and the x-axis. The derivation that I follow in this video is very similar to that for the simpler case but the only difference now is that the rectangular subinterval has a different area and centroid. This leads to slightly different formulas but I show later on in this video that it is in fact a more general case for the simpler case, which is simply the second curve having the function g(x) = 0, which is just the x-axis! This is a great video to further reinforce your understanding of deriving integral formulas and how slightly modifying the starting parameters affects the final formulas, so make sure to watch this video!
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Applications of Integrals: Moments and Centers of Mass: Bounded by Two Curves
In my earlier video I derived the formulas for centers of mass for a region bounded by a function and the x-axis:
In fact we can use the same sort of argument that led to the above formulas but this time to obtain the formulas for the centroid of a region R that lies between two curves y = f(x) and y = g(x) where f(x) ≥ g(x). Doing so will obtain the following formulas:
