Question

The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method.

x = 1 − y^4 x = 0, about the line x = 5
Please see the attempt in the images:
http://i1084.photobucket.com/albums/j409/QRAWarrior/MATA36-IMG008a.png
http://i1084.photobucket.com/albums/j409/QRAWarrior/MATA36-IMG008b.png

I believe I used the disk method and said let r be my radius. I believe I integrated with respect to x and I got the wrong answer...

Answer 1

I think I figured it out:
Would radius be 5 -x, and the height of the cylinder be the function 1 - y^4?

Answer 2

r = 5 - x
r = 5 - (1 - y^4)

Answer 3

h = 1 - y^4

Answer 4

since you are rotating about the line x=5, the disk method makes you integrate wrt y. your washers will be flat

Answer 5

Shell works here right?

Answer 6

I just realized it now that I could make a cylinder...

Answer 7

with height y, and radius 5 - x

Answer 8

it'd be difficult(but not impossible) to do shell with the axis of rotation being x=5 and the graph being x=1-y^4.

Answer 9

Why?