The region in the first quadrant which is bounded by the curve y² =
4x, and the lines x = 4 and y = 0, is revolved about the x-axis.
Locate the centroid of the resulting solid of revolution.
1
Expert's answer
2022-06-09T14:02:10-0400
ANSWER The centroid is (38,0,0)
EXPLANATION
If x0 is fixed, then when rotating the segment {(x0,y,0):0≤y≤2x0} around x-axis, we get a circle : y2+z2=4x0 . So, the resulting solid of revolution is
Now, to calculate integrals over the region Sx we replace the Cartesian coordinates with polar coordinates : y=rcost,z=rsint(0≤t≤2π,0≤r≤2x) . Therefore
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