Use the Geogebra Applet to create a solid through the rotation of graphs around the x-axis.[br][br]Note that all the purple dots in the Graphics1 window are sliders. They don't snap to "clean" values as well as one may like, but precise computation is not the primary goal of the simulation.[br]The axis of revolution can be dragged either above or below the curves as long as f(x) forms the outer surface and g(x) forms the inner surface.[br]You may enter functions into the input fields or just drag the existing graphs in the Graphics1 window.[br]If you'd like to hide the highlighted disk/washer, just drag the highlight slider all the way to the left.[br]Acknowledged, the appearance is a bit cluttered, but hopefully the controls are found to be pretty intuitive.

The region in the first quadrant between [math]f\left(x\right)=6-x^2[/math] and [math]h\left(x\right)=\frac{8}{x^2}[/math] is rotated about the x-axis. Find the exact volume of the generated solid.

The graphs of [math]x=\frac{y^4}{4}-\frac{y^2}{2}[/math] and [math]x=\frac{y^2}{2}[/math] completely enclose a region. Find the volume of the solid formed when this region is rotated [math]2\pi[/math] radians about the y-axis in the interval [c,d].[br]c,d [math]\ge[/math] 0

Find the exact volume of the solid generated when we rotate the region under [math]f\left(x\right)=\frac{2}{1+x^2}[/math], x=0 and x=3 around the y-axis.