BC 2,3
Problem Set #3
(Due Tuesday, September 24)
Name: ______________
Please show appropriate work – no calculator or computers – except to check work done by hand.
Work should be shown clearly, using correct mathematical notation. Please show enough work on all
problems (unless specified otherwise) so that others could follow your work and do a similar problem
without help. Collaboration is encouraged, but in the end, the work should be your own.
Determine which of the following integrals converge and which diverge. Justify your answer clearly
using an appropriate test or method and showing ALL appropriate work.
1)

 /2


0
2)
8 x  3x
2 x3  5 x  1
1
3)
cos x
dx
sin x


0
2
x 2e  x dx
dz
BC 2,3
4)
Problem Set #3
(Due Tuesday, September 24)
Name: ______________
Let R be the region in the plane bounded by the graphs of y  x 2 , y  6  x, and the y  axis. Find
a. Carefully and accurately sketch the graph of the region R.
b.
Find the volume of the solid obtained when R is rotated about the line y  6  x .
BC 2,3
(5)
Problem Set #3
(Due Tuesday, September 24)
Name: ______________
This problem is an AP Problem (2006 #1). You may use a calculator on this problem.
x3 x2 x

  3cos x . Let R be the region in the second
4
3 2
quadrant bounded by the graph of f, and let S be the shaded region bounded by the graph of f and
the line L, the line tangent to the graph of f at x = 0, as shown below.
Let f be the function given by f ( x) 
a. Find the area of R.
b. Find the volume of the solid generated when R is rotated about the horizontal line y  2 .
c. Write, but do not evaluate, an integral expression that can be used to find the area of S.