CALC 2: Area of a Surface of Revolution (WEBASSIGN)?

Question

Consider the following.
x=y+y^3 from 0 to 4

(a) Set up an integral for the area of the surface obtained by rotating the curve about the x-axis and the y-axis.
(i) the x-axis
S= 2piy(sqrt((3y^2+1)^2)+1)dy
(ii) the y-axis
S= 2pi(y^3+y)sqrt((3y^2+1)^2+1)dy

(b) Use the numerical integration capability of a calculator to evaluate the surface areas correct to four decimal places.
(i) the x-axis, the answer is1258.6212
(ii) the y-axis I CAN'T GET THIS ONE.
I got 14536.3874, but I got it WRONG.

Can someone please help me! Thank you

Answer 1

For (ii) Your integral appears to be correct but the answer you have is not correct to four decimal places.  I did the same integral and came up with 14536.38747 rounded to four decimal places is 14536.3875.