Alright, I know there's some smart people here, maybe one of you can help me.

I need to calculate the volume of a solid whose base is (x^2)+(y^2)=2 with the cross sections being squares perpendicular to the x axis.

Well, I'm stuck. The answer I'm getting is wrong. Can someone help me out?

Is that all the information you have?

All that tells you is that the base is a circle of radius sqrt(2)

[edit]
wait... cross sections of what?

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[This message has been edited by lateralus (edited December 07, 2003).]

Cross sections of the solid. The solid is formed by using solid cross sections whose bases are bounded by the equaton given, in this case a circle. It's hard to explain, especially since I barely understand it myself... :/

Solve the equation in terms of x. Then just set up your integration, but use the the volume of a square as part of your integration function...so you would have like this:

Integral of (function you solved for in terms of x)^3

Though I am sure it would be easier to do as cross sections of circles so you would have:

pi * the Integral of (fuction you solved for in terms of x)^2

[This message has been edited by Ubuu (edited December 07, 2003).]

[This message has been edited by Ubuu (edited December 07, 2003).]

I think that is what you do. In our calc class we used the method of disc most of the time, meaning the cross sections are circles. Isnt that the easiest way to get an estimate?

Hmm...well, in this case I am supposed to use square cross sections, so i'll see how this turns out...

If you're integrating to find the volume, technically you're adding up the are of an infinite number of rectangular regions with an infinitely small width. If you wanted you could also do a Riemann Sum with n equal to something moderately large like 8. I think the general rule is disk or washers for x-intergration about a horizontal axis or y-integration about a vertical axis. So I'd solve it for y, but it won't really effect the outcome.