Posted by h on Sunday, September 16, 2012 at 2:16pm.
Find the volume of the solid generated by revolving the region bounded by the line y=5x+6 and the parabola y=x^2 about the following lines:
a) the line x=6
b) the line x=1
c)the x axis
d) the line y=36
Thanks!

Calculus  Steve, Sunday, September 16, 2012 at 3:29pm
the curves intersect at (1,1) and (6,36)
The xline rotations all work the same way. Shells probably work best:
v = ∫[1,6] 2pi * r * h dx
where r is 6x or 1+x and h = (5x+6)x^2
simple polynomial
for the yline axes, maybe discs work best, but you'll have to use washers, since the discs will have holes in them.
v = ∫[1,6] pi * (R^2r^2) dx
where R=(y6)/5 and r = x^2
again simple polynomials to integrate.
Come on back if you get stuck.
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