Let f (x) = cos x and g (x) = sin x. Find the center of gravity (x, y) of the region between the graphs of f and g on[0,π/2].

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Mathematics

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21 December, 01:40

Let f (x) = cos x and g (x) = sin x. Find the center of gravity (x, y) of the region between the graphs of f and g on[0,π/2].

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Garrett Herrera · Answer 1

How do you find the center of gravity of the region between the graphs of f (x) = cosx and g (x) = sinx on [0, pi/2]?

I got Msubx = 0, Msuby = - 2, and Area = 0. But that can't be right, as that would make the center of gravity (-2/0, 0), and that's obviously wrong. I think it has something to do with the areas of cosx and sinx canceling out, but I don't know what to do with it - how do I not get an area of 0? Also, I suspect I made mistakes with Msubx and Msuby but can't figure out where.