# Volume using cross section

• February 5th 2011, 03:13 PM
Wolvenmoon
Volume using cross section
Problem is "The base of a solid is the parabolic region {(x,y)|Y^2<=x<=1} OR from what I can tell x=Y^2 0<=x<=1 ( Answer is 2 )

This means I have a simple base*height problem, it should be the integral from a to b of the area of these squares.

But then I go to set up my integral and I get lost. I know I should have y^2 in there, but what goes with it?

Thanks!

( Edit: How did my entire post cut off? )
• February 5th 2011, 04:01 PM
skeeter
Quote:

Originally Posted by Wolvenmoon
Problem is "The base of a solid is the parabolic region {(x,y)|Y^2<=x<=1} OR from what I can tell x=Y^2 0<=x<=1 ( Answer is 2 )

This means I have a simple base*height problem, it should be the integral from a to b of the area of these squares.

But then I go to set up my integral and I get lost. I know I should have y^2 in there, but what goes with it?

Thanks!

( Edit: How did my entire post cut off? )

assuming the cross-sections are squares perpendicular to the x-axis ...

$x = y^2$ ... $y = \pm \sqrt{x}$

$\displaystyle V = \int_0^1 (2\sqrt{x})^2 \, dx$
• February 5th 2011, 05:28 PM
Wolvenmoon
Thanks! ( I miss that but get fluid force on a dam right. LOL )