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Calc II finding volume of solid by rotating

  • #1

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 dont 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) ?
 

Answers and Replies

  • #2
LCKurtz
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The distance horizontally is always xright - xleft. In this case xleft = -1, so for whichever radius you are doing you are going to use

π(xright - (-1))2 = π(xright + 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.
 

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