Math 1B
Due date: Wednesday 24 February
Name: _________________________
Take Home Quiz 1
Please show all your work on a separate sheet of paper. Neatly do the problems in order and leave enough space between
problems for my comments and grading. You are allowed to get help with the problems and discuss them with your
classmates but all work must be your own.
1. Evaluate each integral.
a)
∫
π
4
0
sin θ
dθ
cos3 θ
b)
∫
x
dx
(x − 2)2
c)
∫
sin(ln x)
dx
x
2. Find the area of the region bounded by y = x − 3 and y =
3. Let R be the region bounded by y = x and y =
d)
ex
∫ 0 1+ e2 x dx
1
1
x.
2
1
x.
2
a) Find the volume of the solid obtained by revolving R about the x- axis. Identify the type of
object made by your typical slice (disk, washer, or shell).
b) Find the volume of the solid obtained by revolving R about the y- axis. Identify the type of
object made by your typical slice (disk, washer, or shell).
4. Let R be the region bounded by y = x , y = 1 , and the y-axis.
a) Set up the integral necessary to find the volume of the solid obtained by revolving R about
the line x = −1. You do not need to integrate, but identify the type of object made by your
typical slice (disk, washer, or shell).
b) Set up the integral necessary to find the volume of the solid obtained by revolving R about
the line y = 2. You do not need to integrate, but identify the type of object made by your
typical slice (disk, washer, or shell).