Megan V.

asked • 02/21/24

Calc center of mass problem

A solid is formed by rotating the region bounded by the curve y=e−5x/2 and the x-axis between x=0 andx=1, around the x-axis. The volume of this solid is π5⋅(1−e−5). Assuming the solid has constant density δ, find x¯ and y¯.

Paul M.

tutor
Your notation isn't clear: is the 2 in the exponent or do you mean 1/2 times the e^(-5x)? Of course the cg in the x-direction is 0 by symmetry, but in the y direction you need clear notation to construct the necessary integral.
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02/21/24

Bradford T.

I found the volume to be (pi/5)(1-e^(-5)), so I question if the problem was copied correctly. y-bar would be zero if the solid is rotated around the x-axis.
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02/21/24

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