Calc II finding volume of solid by rotating

[MillerGenuine]

Homework Statement

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

y=x^2
x=y^2
about x= -1

Homework Equations

Volume= Integral of A(y) dy where A(y)= (pi)(r)^2

The Attempt at a Solution

My question is how to find the radius portion in the (pi)(r)^2
I know that you subtract the inner radius from the outter radius..and the book says that this is
[(y^1/2) - (-1)]^2 - [y^2 - (-1)]^2

I don't understand how they determined that you subtract (-1) from the function, I realize this is the distance from the roatating axis, by why not [(-1) - (y^1/2)]^2 - ...

how do i determine whether i subtract or add the (1) ?

 

[LCKurtz]

The distance horizontally is always x_right - x_left. In this case x_left = -1, so for whichever radius you are doing you are going to use

π(x_right - (-1))² = π(x_right + 1)².

Since the radius is squared it would be OK to subtract in the other way, but it is a good habit to always write it this way.