Finding the Volume of a Rotated Solid Using Partial Fractions

[philsgirl2008]

Homework Statement

Find the volume of the resulting solid if the region under the curve y=1/(x^2+3x+2) from x=0 to x=1 is rotated about the x-axis.
R=(1/(x^2+3x+2)
Equation for volume using the slicing method...
3.14 INT((1/(x^2+3X+2))^2)dx over the interval 0-1

Homework Equations

R=(1/(x^2+3x+2)
Equation for volume using the slicing method...
3.14 INT((1/(x^2+3X+2))^2)dx over the interval 0-1

The Attempt at a Solution

3.14 INT((1/(x+1)^2(x+2)^2))
A/(x+1) + B/(x+2)^2 + C/(x+2) + D/(x+1)^2 = (1/((x+1)^2)(x+2)^2))
1= A(x+1)(x+2)^2 + B(x+2)^2 + C((x+1)^2) + D(x+1)^2
Set x= -1, B=1
Set x= -2, D=1
Where do I go from here?

 

[philsgirl2008]

By the way - sorry this isn't very pretty, never used this site before so I wasn't sure if there was exponential / division things. so that's what it is, Thank you!