Posted by Morgan on .
Find the volume of the solid generated by revolving the triangular region with vertices (1,1), (b,1), and (1,h) about:
a) the xaxis
b) the yaxis

Calculus II 
Steve,
If a<1 and b<1 we get
Using discs:
pi*Int(R^2  r^2) dx [b,1]
R = 1
r = y = (a1)(xb)/(1b) + 1
= pi/3 (a1)(a+2)(b1)
Using shells:
2pi*Int(rh)dy [a,1]
r = y
h = 1x = 1  [(1b)(y1)/(a1) + b]
= pi/3 (a1)(a+2)(b1)
If a or b > 1, then change integration limits and (1a) > (a1), but the answer is the same
Thank you, Wolframalpha! 
Calculus II  PS 
Steve,
oh  that's just around the xaxis. Good luck on the yaxis. By symmetry, the results should look quite similar.