Set up the simplified integral and compute the volume created when the area bounded by one period of the function 3+sin(x) and the x-axis (use the endpoints of the period starting at x=0) is rotated around:
a) the x-axis
b) the y-axis
inverse trig functions are nasty, so we will try to use dx in both cases.
around the x-axis use discs (washers) of thickness dx,
v = ∫[0,2π] πr^2 dx
where r = 3+sinx
v = ∫[0,2π] π(3+sinx)^2 dx
around the y-axis, use shells of thickness dx
v = ∫[0,2π] 2πrh dx
where r = x and h=y=3+sinx
v = ∫[0,2π] 2πx(3+sinx) dx