SMITH, Unknown, Staff, Donald, JUHA, kim, TatsuhikoHatase, Peters, Al-Hammali,H., ArachchiAppuhamillage,T., Artz,J., Hoewoon Kim, Dr. Orum, Sarah Hagen
Part I. Multiple Choice Questions (5 points
Instructions: For each multiple choice questior,
each)
clearlSr circle your answer on the test page,
(1) Circle either TRUtr or EALSE for the following stat
5.4: Working with Integrals
With the Fundamental Theorem of Calculus, we can now compute all sorts of definite integrals. In this section, we discuss a few properties of integration.
Even and Odd Func
5.5: Substitution Rule
We know that antiderivatives take functions in the opposite direction as derivatives. We
have seen several antiderivative rules based on corresponding derivative rules such as s
7.7: Numerical Integration
Up to this point, we have learned all sorts of techniques for computing the antiderivatives
of given functions. But not all functions have nice antiderivatives. For such fun
Math 252
Practice Final Exam - Part 2
Name:
You will have 50 minutes to complete the exam. You may use a non-graphing calculator and a 3 12
inch note card. Please draw a box around your final answers.
5.1: Approximating Areas Under Curves
In differential calculus, we saw that the derivative of a function told us the slopes of the
tangent line. Similarly, in integral calculus, we define the integral
7.1: Basic Approaches
Before we begin looking at more integration techniques, we review some of the techniques
we learned in chapter 5, and look at some tricks that can help us rewrite the integrand s
MTH 252 Quiz 1
Name: M.
Show all your work in your answer for full credits.
1. (4 points) Evaluate the following indenite hitegral.
l
flxdz
I
Hint: Rewrite the integral in simplied form and use the fa
6.3: Volume by Slicing
So far, we have seen that we can use integration to compute the area of two-dimensional
regions bounded by curves.
Integrals can also be used to compute the volumes of three-dim
Math 252
Practice Final Exam - Part 1
Name:
You will have 50 minutes to complete the exam. You may use a non-graphing calculator and a 3 12
inch note card. Please draw a box around your final answers.
5.2: Definite Integrals
In the previous section, we saw that Riemann sums for f on [a, b] give approximations to
the actual area of the region bounded by the graph of f . We also saw that the accuracy
mth252 Integral Calculus
Practice Problems for Midterm Exam
l-
Midterm Exam 1 covers Section 4.9 through 6.1. The following are all problems you should be able to do on your own without a calculator (
5.3: Fundamental Theorem of Calculus
Previously, we saw that the area bounded by the graph of a function f (t) over the interval
[a, b] was given by
Z b
f (t)dt.
a
Using that, we can define a function
7.2: Integration by Parts
In section 5.5, we derived the Substitution Rule from the Chain Rule of differential calculus.
Similarly, we can use the Product Rule to derive a new method of integration.
I
Part I. Multiple Choice Questions (6 points each)
Instructions: For each multiple choice question, clearly record your answer
on the previous
page.
(1) Circle either TRUE or FALSE for the following st
12. A fisherman is about to reel in a 14-lb fish located 13 ft directly below him. If the fishing line weighs
1 oz per foot, how much work will it take to reel in the fish? Round your answer to the ne
mth252 Integral Calculus
Practice Problems for Midterm Exam
1
Midterm Exam 1 covers Section 4.9 through 5.5. The following are all problems you should be able to do on your own without a calculator (a
7.8: Improper Integral
So far, every definite integral we looked at has been over a finite interval [a, b]. But what if
we wanted to take the integral over an interval of an infinite length?
Z
2
How
7.5: Partial Fractions
Given
Z
2
1
x1 x+2
dx,
by the substitution rule, we can evaluate this integral and get
Z
1
2
x1 x+2
dx = 2 ln |x 1| ln |x + 2| + C.
But if we are given
Z
x2
x+5
dx,
+x2
the an
7.4: Trigonometric Substitution
When we studied the arc length of curves, with the technique we had at the time, the types
of functions we could study were very limited.
For instance, we were not able
6.7: Physical Applications
In this section, we see many ways in which we can apply integral calculus to solve real life
problems.
We compute things like mass, total force, and work. Things you may see
Math 252
Practice Midterm
Name:
You will have 50 minutes to complete the exam. You may use a non-graphing calculator and a 3 12
inch note card.
1. Calculate the antiderivative.
Z
2x +
x3
dx.
x
2. Nea
6.1: Velocity and Net Change
We have seen several techniques of integration, so it is now time to start applying what we
have learned to solve problems.
Velocity, Position, and Displacement
In differe
7.3: Trigonometric Integrals
In previous section, we saw the antiderivative of sin2 (x). But what if we need the antiderivative of a higher power sine function? How do we compute the antiderivative of
4.9: Antiderivatives
As we have seen, the point of integration is to do the opposite of differentiation. So just like
with derivatives for differential calculus, there are antiderivatives for integral
6.4: Volume by Shells
We have seen two related methods disk and washer of computing solids of revolution.
However, these two methods can be difficult to use when we have a solid like the one we
would
mth252 Integral Calculus
Practice Problems for Midterm Exam 1
Midterm Exam 1 covers Section 4.9 through 6.1. The following are all problems you should be able to do on your own without a calculator (w
Basic Integral Table
k is any nonzero constant
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
k f (x) dx = k f (x) dx
( f (x) + g(x) dx = f (x)
( f (x) g(x) dx = f (x)
p
x dx =
dx
MTH 252 Midterm 2 Review/ Practice Problems Spring 2015
Skip problems 12, 13(a), and 14. These are from 6.8
These are some problems to work on in preparation for the second midterm on Tuesday,
May 12,
MTH 252
SAMPLE FINAL EXAM
NAME :
OSU ID:
Instructor: Torrey Johnson
No Calculators.
No cell phones, laptops, tablets or other such devices may be used.
A 5x8 inch note card is allowed (both sides), OR