Find the volume of the solif generated when the region enclosed by x=y(1-y^2)^1/4, y=0, y=1, and x=0 is revolved about the x-axis.

Question

anonymous · Answer

do i solve for y?

mathteacher1729 · Answer

Give me a few minutes... I'm doing some other stuff right now, but I will come back later. 

Hint:  Sketch the region and then determine if your cross section will be PARALLEL to the axis of rotation or PERPENDICULAR to the axis of rotation.

anonymous · Answer

Thank you

anonymous · Answer

$$x= y(1-y^2)^{1/4}$$

mathteacher1729 · Answer

Here's the region of integration. Notice that it's easier to work with if your cross section is PARALLEL to the axis of rotation (the x-axis). (method of "cylinders") http://tutorial.math.lamar.edu/Classes/CalcI/VolumeWithCylinder.aspx

anonymous · Answer

so it's shell method?

mathteacher1729 · Answer

Yeah.  The key with these kinds of problems is to ask yourself "is the cross section PARALLEL to the axis of rotation... or PERPENDICULAR to the axis of rotation?"

anonymous · Answer

do i just leave the equation in terms of y