Hello, I'm trying to find the Volume of this solid by the Shell Method but can't figure out what the height of the shell is for this:

rotation about x-axis of region bounded by y=x^2 and y=6x+7

 

the formula should be:

Volume= 2pi int(radius*height) dy from 0 to 49. I know radius is y. But what is the height?

Edited October 21, 201114 yr by dominet

-- sorry, I misunderstood --

Edited October 21, 201114 yr by Wuz Here

Annnd I just answered my own post again: divide the volume into 2 volumes (first from y=0 till y=1, second from y=1 till y=49) then add them.

In other words:

http://www.wolframal...+dy+from+0+to+1

++++Plus++++

http://www.wolframal...dy+from+1+to+49

Edited October 21, 201114 yr by dominet

Annnd I just answered my own post again: divide the volume into 2 volumes (first from y=0 till y=1, second from y=1 till y=49) then add them.

In other words:

http://www.wolframal...+dy+from+0+to+1

++++Plus++++

http://www.wolframal...dy+from+1+to+49

 

gratz

 

Briggs & Cochran Calculus: Early Transendentals gives a good description of the shell method as well!

 

[math] V = \int^b_a 2 \pi x ( f(x) - g(x) ) dx [/math]

Edited October 21, 201114 yr by Wuz Here