Shell Method Problem: Solve x=y^(2), x=4 About the X-Axis

[hvidales]

Homework Statement

x=y^(2), x=4, about the x axis.

Homework Equations

2pi* integral from a to b of radius*height of function*thickness

The Attempt at a Solution

I have 2pi* integral from -2 to 2 of y*(4-y^(2)) dy but that does not make any sense. Answer comes out to be 0. The real answer is 8pi. I know how to do this with the disk method just not the shell method. Thank for the help!

 

[tiny-tim]

hi hvidales!

… integral from -2 to 2 …

noooo

 

[hvidales]

I see and thanks. However, how come for this problem: y=x^(2), y=2-x^(2), about x=1 the limits are from -1 to 1 ?

 

[tiny-tim]

you mean x goes from -1 to 1?

that's because the body in that case goes from x = -1 to x = 3 (the reflection about x = 1)

in your first example the body went from y = -2 to y = 2

in each case, you're taking half (because each single cylindrical shell is in both halves)

 

[hvidales]

Thank you!