calculus
posted by jump .
determine the volume of the solid of revolution generated by revolving the region bounded by y=x^3x^5, y=0, x=0 and x=1 about the line x=3

check to be sure that the graph lies all on one side of the axis for the interval. It does.
So, volume is
v = ∫[0,1] pi (R^2r^2) dx
where R = 3, r = 3y
= pi∫[0,1] 9  (3(x^3x^5))^2 dx
= pi∫[0,1] x^10 + 2x^8  x^6  6x^5 + 6x^3 dx
= pi(1/11 x^11 + 2/9 x^9  1/7 x^7  x^6 + 3/2 x^4) [0,1]
= 677/1386 
*pi