Could somebody help me out on this? It's an applications of integration problem based on using cross sectional areas to find the volume of a solid. One moment.

Question

mendicant_bias · Answer

"The solid lies between the planes perpendicular to the x-axis at x = 0 and x = 4. The cross sections perpendicular to the axis on the interval $$0 \le x \le 4$$ are squares whose diagonals run from the parabola 
$$y = -\sqrt{x}$$to the parabola $$y = \sqrt{x}$$."

This is how i'm physically imagining this:

mendicant_bias · Answer

Damn, this is really hard to draw via Openstudy to try to show three dimensions...

mendicant_bias · Answer

Okay, i'm having trouble drawing what I see just due to how convoluted it would look on Openstudy's drawing pad, but i'll describe it instead: At x = 4, i'm imagining that the end of a diagonal of one of the cross sections is at y = -sqrt(x) and runs to the other end of its own diagonal, ending at y = sqrt(x).

mendicant_bias · Answer

i.e., the diagonal of the square cross section is entirely perpendicular to the x-axis like so:|dw:1366635081134:dw|