The question is to find the volume of the region bounded by y = 5 and y = x + (4/x), rotated about x = -1.
I used the cylindrical shell method but my answer doesn't match the textbook answer.
My method: y = 5 intersects the curve at x = 1 and 4.
V = integrate (2*pi*(x+1)*(x + (4/x)) dx from x = 1 to 4. = 2*pi*integrate(x^2 + 4 + x + (4/x)) from 1 to 4 = 2*pi*[ (1/3)(x^3) + 4x + (1/2)(x^2) + 4ln|x| ] from 1 to 4 = pi*(81 + 8ln|4|) which is clearly different from the given answer 8*pi*(3-ln4).