Volume of Solids of Revolution

Econometricia

Find the volume of the solid st,
1. y=cos x , y= 0 in [0,pi] ; Rotated around x=1



2. I am slightly confused, I see that the area will double around twice so I can just use the left half of the curve. I am just not sure how to do so.

Mark44

Are you sure that you copied this problem correctly. The line x = 1 does not divide the region between y = cosx and y = 0 into two equal halves, so rotating it around the line x = 1 makes a complicated volume of revolution. Could it be that you're supposed to rotate the region around the line y = 1?

Econometricia

Yes, not 2 equal halves but the rotation around the x=1 axis would cover the right hand side of the curve in rotation and double over so cant we ignore that piece?

Mark44

No, I don't think so. The part of the region under y = cosx on [0, 1] would cover the part on [1, pi/2], so I suppose you could ignore that part. The part of the curve on [pi/2, pi] is below the x-axis. The part above [0, 1] is above the x-axis. This is a very unusual problem.