Find the volume of the solid generated by rotating the region of the x-y plane between the line y=6, the curve y=3sin(x)+3 for -pi/2 < (or equal to) x < (or equal to) 5pi/2 about the line y = 6.

Answer 1

best to use discs of thickness dx. So,

v = ∫πr^2 dx
where r = 6-y. So,
v = ∫[-π/2,5π/2] π(6-(3sinx+3))^2 dx
= 81π^2/2