Method of Discs/Washers and Cylinderical Shells

[trogdor5]

There's just something I need cleared up. When rotating around a line that isn't the x or y axis,I'm not quite sure what to do. Here are some problems:

1) Find the volume of the solid that results when the region enclosed by y=√x, y=0, and x=9 is revolved around the line x=9.

2) Find the volume of the solid that results when the region enclosed by x=y² and x=y is revolved about the line y=-1

3) Use cylindrical shells to find the volume of the solid that is generated when the region that is enclosed by y=1/x^3 , x=1, x=2, y=0 is revolved about the line x=-1

I know that with the cylindrical shells the alteration is within the X part of the formula (2π∫x*f(x)dx) but I'm not exactly sure how to alternate the other two. For example, if the function is √x will the thing become √(x+1)^2 or [(√x)+1]^2? If you could just show me how to do each problem, that would solve my problems :) I know you guys aren't supposed to show how to do the problem, but the only way you can answer my questions is with showing mehow to do it :)

Thank you.

 

[vela]

Start by drawing a picture.

 

[tiny-tim]

Hi trogdor5!

(try using the X² tag just above the Reply box )

… For example, if the function is √x will the thing become √(x+1)^2 or [(√x)+1]^2?

If you're changing x, then you're replacing x by x - a, so y = √x becomes y = √(x - a).

If you're changing y, then you're replacing y by y - a, so y = √x becomes y - a = √x.