Find the volume of the solid obtained by rotating the region bounded by y = l n x ,

mybabe43nncck

mybabe43nncck

Answered question

2022-06-03

Find the volume of the solid obtained by rotating the region bounded by y = l n x, y = 0, x = 2 about the x-axis
I ended up with 2 π 1 2 ln ( x ) d x
I would like to know if this is the correct way to set this problem up given the bounds.

Answer & Explanation

Bruce Townsend

Bruce Townsend

Beginner2022-06-04Added 5 answers

If it is the finite region bounded by the lines y = 0, x = 2, and the curve y = ln x, and we are rotating about the x-axis, then the volume is
1 2 π ( ln x ) 2 d x .
For take a slice of the solid at x. Then the radius of cross-section is y, that is, ln x, so the area of cross-section is π ( ln x ) 2
Remark: If you want to use cylindrical shells instead, then we get the expression
0 ln 2 2 π y ( 2 e y ) d y
for the volume.

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