Integration problem regarding finding the volume of a solid given equations depicting its shape, 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 (a). the x-axis, (b). the y-axis, (c). the line x = 1, and (d). the line y = 3."

I really don't have any clue to start with this one.

mendicant_bias · Answer

I'm aware that the general formula for the volume of some object is$$V = \int\limits_{a}^{b}A(x)dx$$And i'm capable of doing that with linear objects, not quite sure how to find a cross section of the area of one of these to do this properly.

amistre64 · Answer

helps to start with a sketch of the regions defined

mendicant_bias · Answer

None given, and I don't think this will look dandy in three dimensions on Openstudy's drawing software, lol. I'll take a crack at drawing it, but it's less of understanding where things are that's making me unaware than understanding how to find the cross sectional area of a shape that isn't a traditional geometrical shape. One minute.

mendicant_bias · Answer

|dw:1366824380463:dw| (Where the parabolic looking thing is just a section of y = 3x^4 bounded at x = -1, x = 1