Find the volume of the solid obtained by rotating the region bounded by… (Calculus II)?
Find the volume of the solid generated by rotating the region bounded by the x-axis, the curve y=3x^4, and the lines x=1 and x= -1. The axis of rotation is the y-axis.
My calculus prof is a nightmare, and I'm pretty sure the way she taught us how to approach the problem is wrong. I am using washers method. Prof said that somewhere in the problem one would have to use substitution, but I don't think that's the case. Anyways, if anyone could please go over this problem and send me some feedback that would be great. I came up with a result of 14pi/3.
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put equation in terms of x, for y 0 to 3, use
volume = pi* integral of f(y)^2 dy from 0 to 3
chente
Use a double quintessential. the first quintessential calculates the area below the curve. the 2d quintessential calculates the area you calculated before over a span of 360degrees (a rotation). so it may be: quintessential(0,2pi) quintessential (0,3) y dx dtheta, the position y is the equation you've above.