Volume of a solid using shell method: y=x. , y= -x/2 , x=2 about y-axis

[Math lover799]

Use the shell method to find the volume of the solids generated by revolving the region's blunderbuss the curves and lines about the y axis.

y=x. , y= -x/2 , x=2

So I tried answering this question using x as shell radius and (x-x/2) as shell height. After integrating I got 8π/3 as the answer. But I checked the solution and they have talked (x-(-x/2)) as shell height. Why have they subtracted it?

 

[tkhunny]

Use the shell method to find the volume of the solids generated by revolving the region's blunderbuss the curves and lines about the y axis.

y=x. , y= -x/2 , x=2

So I tried answering this question using x as shell radius and (x-x/2) as shell height. After integrating I got 8π/3 as the answer. But I checked the solution and they have talked (x-(-x/2)) as shell height. Why have they subtracted it?

?? Why have you added it? The distance between two curves is obtained by subtraction. Maybe I'm not understanding your question.

 

[tkhunny]

Take two numbers, say 10 and 2.

Is the distance between them 10+2 = 12 or 10-2 = 8?