x = 1/3 * (y^2 + 2)^(3/2), 1 <= y <= 2
Correct final answer:
21/2 * pi
SA = 2pi * integral y ds = 2pi*integral (y * sqrt(1 + (dx/dy)^2)) dy
x = 1/3 * (y^2 + 2)^(3/2)
dx/dy = y*sqrt(y^2 + 2)
Then I'm stuck. Wolfram also says my answer is wrong. I used y variables and the y limits of integration and the answer differs from that of the back of the book. (http://www.wolframalpha.com/input/?i=integrate(sqrt(1+%2B+y^4+%2B+y^2)*y)+*+2pi+from +1+to+2)
Any help would be GREATLY appreciated!
Thanks in advance!
I have a 2 where you don't. Perhaps I'm wrong (i didnt go over it lol) and if I am, then you messed up the integration. If not, then try again with that equation
...The rotating about the y-axis means we have
recompute with the new dS.