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princeofpowerjr
10.06.2021 •
Mathematics
Consider the functions
f(x) = xn and g(x) = xm
on the interval [0, 1], where m and n are positive integers and n > m. Find the centroid of the region bounded by f and g.
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Ответ:
Assuming the region is of uniform density, compute the mass of the region and its moments.
If n > m, then in the interval [0, 1] we have f(x) ≤ g(x). This means the mass is
The moments are
Then the centroid is
Ответ: