Study Guide, Chapter 8: The following are similar to integrals on
past tests:
1. 
(Parts)
2. 
or 
(Separate into two
fractions; integration by substitution)
3. 
(Integration by Parts)
4.
Find the volume of the solid formed when the region bounded by y=e−2x,
y=0, x=0, x=ln(3) is revolved about
a. the y-axis.
[Evaluating the integral requires integration by parts]
b. the x-axis
5. 
(Remember the
identities for sin2x and cos2x)
6. 
(Trig integrals)
7. 
or
or 
(Trig sub)
8. 
(Start with long
division)
9. 
(Partial fraction -- possible take-home question)
10.
Evaluate an integral using a formula from a table of integrals. [for an in-class
question, the formula will be given; as a take-home question, the student will
have to find the formula in the table of integrals, after u-substitution]
11.
Evaluate the integral of the function defined by the following table,
using the trapezoidal rule, or Simpson's rule:
|
|
x |
f(x) |
|
|
3 |
0 |
|
|
5 |
3.00 |
|
|
7 |
7.65 |
|
|
9 |
13.39 |
|
|
11 |
20.00 |
12.
Consider the region under the curve y=
above the x-axis, on the interval 1£x<¥.
a. Sketch the region,
b. Calculate its area,
c. Calculate the volume of the solid
formed by revolving the region about the x-axis.
d. Set up, but do not
calculate, the integral for the length of the curve from x=1 to x=10.
Note:
You must know how to set up the integrals for
a. Areas (based on vertical rectangles)
b. Areas (based on horizontal rectangles)
c. Volumes
of revolution (disk or washer method)
d. Volumes of revolution (cylinder method)
e. Arc Length (using x as the variable of
integration)
f. Arc Length (using y as the variable of
integration)
Return to: Merced College; Don Power
Updated 10/08/07 by Don Power