Math Help - I need help setting up these equations for using shell method to find volumes.

1. I need help setting up these equations for using shell method to find volumes.

i am trying to make up my own equations for shell method and completely forgot how to do them. because we did them earlier in the year and have relied mainly on disc method.

My original function will be y=x^2. i have to include revolving around the x-axis, y-axis, x=a, and y=a and have to use the same example with each method. i have came up with

y=x^2, y=0, x=2 revolve around y-axis
y=x^2, y=0, x=2 revolve around x= 3
x= sqr(y), y=0, x=2 revolve around x-axis
x= sqr(y), y=0, , x=2 revolve around y= 4

*integral for first two will be from 0 to 2 and for the last 2 will be from 0 to 4
*i am not sure if they will even work because i am having to make up my example

what would be the p(x)h(x) or p(y)h(y) for each of those?

2. Originally Posted by nuwin
i am trying to make up my own equations for shell method and completely forgot how to do them. because we did them earlier in the year and have relied mainly on disc method.

My original function will be y=x^2. i have to include revolving around the x-axis, y-axis, x=a, and y=a and have to use the same example with each method. i have came up with
see here

i will use the shell method for all. all integrals will be written in the form: $V = 2 \pi \int_a^b (\text{radius})(\text{height})~dx$

y=x^2, y=0, x=2 revolve around y-axis
$V = 2 \pi \int_0^2 (x)(x^2)~dx$

y=x^2, y=0, x=2 revolve around x= 3
$V = 2 \pi \int_0^2 (3 - x)(x^2) ~dx$

x= sqr(y), y=0, x=2 revolve around x-axis
$V = 2 \pi \int_0^4 (y)(2 - \sqrt y) ~dy$

x= sqr(y), y=0, , x=2 revolve around y= 4
$V = 2 \pi \int_0^4 (4 - y)(2 - \sqrt y) ~dy$

be sure that you can identify what i used for the radius when we are not going about either of the axis. in the shell method, there are only 3 forms for the radius, and it does not depend on the function. you can memorize them. (they make sense, so you can figure them out too. so make sure you know them)