the region bounded by y=5 and y=x+4/x is rotated about the line x=-1, find the volume the resulting solid by any method

Question

sidsiddhartha · Answer

first find the intersection of the curves

sidsiddhartha · Answer

5 = x + 4/x 
so solve it
x^2 - 5x + 4 = 0 
(x - 1) (x - 4) = 0 
x = 1, 4 
now u can solve it using shell method

sidsiddhartha · Answer

sidsiddhartha · Answer

now think the solid as a set of cylindrical shells one inside other
now what it the hieght of each shell?

sidsiddhartha · Answer

it is simply distance between y = 5 and y = x + 4/x

anonymous · Answer

yeah i know i need to find intersections. the problem that i have is i cant find the correct p(x) and h(x). Could you help me out? Thanks so much.

sidsiddhartha · Answer

so H=5-x-4/x
and radius R=(x+1)
now volume
$$\int\limits_{1}^{4}2 \pi RH=volume$$
$$volume=\int\limits_{1}^{4}2*\pi *(5 - x - 4/x)(x+1)dx$$

anonymous · Answer

oh i see! i got the wrong boundaries. thanks so much! that really helped!

sidsiddhartha · Answer

:)