The question:
Find the volume of the solid generated by rotating the region bounded by y=0 and y=sqrt(x) around the line x=6.
My approach (1):
integrate w.r.t to y.
integrate limit from 0 to sqrt(6) of integrand pi*(y)^4 dy.
pi*(y^4) because radius would be y^2 and area would be pi*(y^4).
This gave the answer in decimal 55.4.
My approach(2):(USE SHELL METHOD) So radius would (6-x)
height would sqrt(x)
width would be dx
so integrate limit from o to 6 of integrand (2*pi)(6-x)(sqrt(x))dx
The answer you get in decimal 147.75.
2 completely different answers from the 2 valid methods in my view. Can anyone please explain where I went wrong. The second answer is the correct one.