Solution:
Given, f(x)=y=2−x2
Since, it is revolving around y-axis, centroid will lie on y-axis.
So, it is of the form C(0,y,0).
y=2∫abf(x)dx∫0bf2(x)dx=2∫02(2−x2)dx∫02(2−x2)2dx
=2∫02(2−x2)dx∫02(4+x4−4x2)dx
=2(2x−x3/3)02(4x+x5/5−4x3/3)02
=2(22−(2)3/3)(42+(2)5/5−4(2)3/3)
=2(22−(22)/3)(42+(42)/5−8(2)/3)
=54
Now, C(0,54,0)
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