http://postimg.org/image/q3u3faqoj/
Please advise how to solve without using the shell method.
What other volume methods have you tried so far?
You can solve for x in terms of y and do a disk/washer method.
shell method would be the simplest, the equation being just 2pi * the integral from 0 to 2 of (x*(3x-x^2))
you can also use the disks method by finding x in terms of y.
x1=sqrt(9-y)
x2=(9-y)/3
x3= 2
using x1, x2, and x3 for readability.
graph these 3 functions or solve for points of intersection manually if you cant use graphing calculators, split integrals accordingly
integral from 3 to 5 of ((x3)^2 - (x2)^2) + integral from 5 to 9 of ((x1)^2 - (x2)^2)
I have tried washer method but it didn’t work. @RHSclassof16
woops, i forgot to multiply by pi in my answer above.
@APScholar18 Did you make sure you solved for x in terms of y and changed your upper and lower limits on the integral to be y values instead of x values?
yes @RHSclassof16 do you mind helping work this out for me. The answer is 8 pi btw.
@buddypls I don’t understand why you split the integral.