# Volume using shell method

1. Feb 1, 2013

### whatlifeforme

1. The problem statement, all variables and given/known data
Find the volume of the solid generated by revolving the region bounded by y=4x-x^2 and y=x about the y-axis and about the line x=3.

2. Relevant equations
1. y=4x-x^2 and y=x
2. y=4x-x^2 and x=3

3. The attempt at a solution
1. 2∏∫ (0 to 3) (x)(4x-x^2 -x) dx
2. 2∏∫ (0 to 3) (3-x)(4x-x^2 -x) dx

2. Feb 1, 2013

### HallsofIvy

Staff Emeritus
Obviously you need to go ahead and actually subtract that last "x" in each formula: $2\pi\int_0^3 x(3x- x^2)dx= 2\pi\int_0^3 3x^2- x^3 dx$ and $2\pi\int_0^3 (3- x)(3x- x^2)dx= 2\pi\int_0^3 9x- 6x^3+ x^3 dx$ but, yes, those are set up correctly.

3. Feb 1, 2013