Same problem as before with a different rotational axis. Never done one like this before. (Posted below in a moment).

Question

mendicant_bias · Answer

"Find the solid's volume generated by revolving the region bounded by the x-axis, the curve y = 3x^4, and the lines x = 1 and x = -1 about the line x = 1."

mendicant_bias · Answer

$$V = \int\limits_{a}^{b}A(x)dx$$ As presumed knowledge. I'm assuming i'll have to use the washer method but a little confused about how to go about it; the area for the "inner" portion could be calculated, but I don't get how to solve the other.

mendicant_bias · Answer

With the addition of that "outer" part of the U-shape, it kind of just looks like a half-pipe going in a complete circle.

anonymous · Answer

I think if you can find the volume of the inner portion, you can get the volume of the other by just substracting that from the cylinder that holds them both

mendicant_bias · Answer

God, i'm being painfully incoherent at the moment. EDIT: (The inner portion meaning If half of this U-shaped object was rotated around one of its bounds, basically making what would look like the bell of a brass instrument or something, splaying out. This could be calculated using the Disk or Shell method in ways I know. Not sure how to calculate the "outer" portion, which would resemble half an inner tube).

mendicant_bias · Answer

That actually makes sense. Well, okay. I'll come back to this, but i'm headed to dinner; thanks for the time being.