Verify my answer for finding a volume

[hank]

Using cylindrical shells, find the volume of a solid generated when the region enclosed by following is revolved aobut the y-axis:

y = 2x - 1, y = -2x + 3, x = 2

Setup:

V= 2pi S[1 to 2] x(2x - 1) dx
= 2pi S[1 to 2] 2x^2 - 1 dx
...
=19pi / 3

The book says the answer is 20pi/3.

Just wondering if the book is wrong or if my setup is wrong.

Thx..

 

[galactus]

\(\displaystyle \L\\2{\pi}\int_{1}^{2}x((2x-1)-(-2x+3))dx\)

 

[hank]

Brilliant!

That makes so much sense!

Thank you!!!