Calculus II
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

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! 
oh  that's just around the xaxis. Good luck on the yaxis. By symmetry, the results should look quite similar.