Millersville University Name
Department of Mathematics
MATH 211, Calculus II, Homework 2
February 19, 2008
Please answer the following questions. Partial credit will be given as appropriate, do not
leave any problem blank. Each problem is worth ten points. Your completed assignment
will be due at class time on Monday, February 25, 2008.
1. Determine whether the following improper integrals converge or diverge. For those
that converge, give their value.
(a) Z1
0
1
(x−1)2/3dx
(b) Z∞
−∞
x
(1 + x2)3dx
(c) Z0
−1
1
3
√2x+ 1 dx
2. Find the area bounded between the graphs of f(x) = cos xand g(x) = sin xfor
−π/2≤x≤π/2.
3. Find the volumes of the following solids of revolution.
(a) The region bounded between y=x2and y=x3in the first quadrant is revolved
around the line y= 1.
(b) The region bounded between graphs of y= 2 −√x,y= 1 + √x+ 1, and x= 4
is revolved around the y-axis.