Question

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
y=2+1/x^4,y=2,x=4,x=9;
about the x-axis.

Answer 1

Int(2 + 1/x^4 - 2 dx)[4,9]
= -1/3 x^-3 [4,9]
= -1/3(1/729 - 1/64)
= 665/139968
= 0.00475

Answer 2

Sorry - we wanted a solid

v = Int(pi (R^2-r^2) dx)
where R = y = 2+x^-4
and r = 2

pi*Int(2+x^-4)^2 - 4 dx [4,9]
pi*Int(4+4x^-4 + x^-8 - 4 dx)[4,9]
pi*Int(4x^-4 + x^-8 dx) [4,9]
-pi*(28/x^3 + 1/7x^7)
= 0.0597

Answer 3

thank you soo much! :D

Answer 4

Hmm. I didn't see where you specified an axis. I rotated around the x-axis.