Math 1220-002
Camacho
Fall 2012
Midterm #1 Review
Logarithmic & Exponential Functions
Definition:
Rules:
1.
2.
3.
4.
and
5.
and
Differential Equations

Understand and use the exponential growth formula:

Use separation of variables to solve differential equations. Especially the following:
o Exponential Growth Equation
o Newtown’s Law of Cooling

Use the integrating factor technique to solve linear first order differential equations:
o

Solve for the integration constant, C, using an initial condition.

Extract appropriate information from a word problem to write down and solve an
appropriate differential equation and answer any questions about the model.
Math 1220-002
Camacho
Fall 2012
Midterm #1 Review
Inverse Trigonometric Functions
1.
and
2.
and
3.
and
Also keep in mind that….
1.
2.
3.
Hyperbolic Functions
Definitions:
Rules:
1.
2.
3.
4.
Math 1220-002
Camacho
Fall 2012
Midterm #1 Review
Basic Integration Techniques
1. Familiarity: Recognize the integrand as the derivative of a familiar function.
2. Simplification: Algebraically simplify the integrand as much as possible before
attempting to integrate.
3. U-Substitution: Let u equal some function of x. Then calculate du in terms of dx.
Finally, substitute so that the integral is in terms of u. Solve the integral in terms of u.
Then substitute x into the solution.
4. Combination: Some problems require some combination of the three techniques
above.
Integration By Parts

o Know how to set u and dv appropriately to find a solution.

Tabular Integration
o Understand the process.
o Know how to set u and dv appropriately to find a solution
o Know when to stop integrating and differentiating.
Trigonometric Integrals
Use various trigonometric identities as well as u substitution and algebraic simplification in
order to solve integrals of the following forms:
1.
2.
3.
4.
Math 1220-002
Camacho
Fall 2012
Midterm #1 Review
It will be helpful to know the following trigonometric identities:

Pythagorean Identities:
o
o
o

Power Reduction Identities
o
o

Product to Sum Identities
o
o
o
Rationalizing Substitutions
You should be able to solve integrals having the following terms by using the corresponding
substitutions




Math 1220-002
Camacho
Fall 2012
Midterm #1 Review
Practice Problems
Logarithmic & Exponential Functions:
Section 6.1:
Section 6.3:
Section 6.4:
#3 – 14, 15 – 26
#3 – 10, 11 – 22, 37 – 44
#17 – 26, 27 – 33
Differential Equations:
Section 6.5:
Section 6.6:
#1 – 4, 5 – 24, 39 – 45
#1 – 14
Inverse Trig & Hyperbolic Functions:
Section 6.8:
Section 6.9:
#39 – 54, 55 – 72
#13 – 37, 38 – 45
Integration Techniques
Section 7.1:
Section 7.2:
Section 7.3:
Section 7.4:
#1 – 54
#1 – 36, 37 – 48
#1 – 30
#1 – 16, 17 – 26