# Math Insight

### Overview of: Integration exam

The integration module exam for Math 1241 is based on part 5 from the Math 1241 thread.

#### Material for the exam

1. Solving pure-time differential equations

1. Calculate a general solution to a pure-time differential equation as an indefinite integral, including an arbitrary constant.
2. Given an initial condition, determine the value of the constant, resulting in a specific solution.
3. Given a graph of the right hand side of a pure-time differential equation (e.g.,, a graph of $f(t)$ for the equation $\diff{x}{t} = f(t)$), sketch a graph of the solution. Be sure that your sketch matches the initial condition, as well as the intervals where the solution is increasing or decreasing.
4. Estimate the solution to a pure-time differential equation using the Forward Euler algorithm.
2. Integration

1. Calculate an indefinite integral as an antiderivative, including an arbitrary constant.
2. Calculate a definite integral, resulting in a single number. Use the Fundamental Theorem of Calculus to determine that single number from the indefinite integral.
3. Estimate a definite integral using a left or right Riemann sum.
3. Applications of integration

1. Compute the area between the graph of a function and the $x$-axis.
2. Use an integral to calculate the average of a quantity over an interval.
3. Use a pure time differential equation to solve for population size as a function of time.

#### Study aids

1. Review problems

All questions that may appear in the integration exam are available so that you can practice them. In both these problems and on the actual exam, the set of problems as well as values of numbers, variables, parameters, and other quantities are selected randomly. You will want to generate multiple versions of the problems to see the larger array of problems. Given the random nature, we cannot guarantee that you will actually see all the problems that will appear on the exam. But the more problems you work on, the greater the chance you will work on problems that will show up on the test.

1. Practice questions

Review questions: Pure-time differential equation problems and Review questions: Integration problems contain problems that reflect the format of questions as they would appear on the exam.

2. Quizzes

Online quiz: Quiz 7, and Online quiz: Quiz 8 are good practice.

2. Problem sets

The problem sets from the Math 1241 thread are also good review.

#### Exam rules

1. You must bring your University ID card.
2. You are allowed 50 minutes to take the exam.
3. You are allowed to have one-half of one letter (8.5in $\times$ 11in) sized sheet of paper of handwritten notes. Double-sided is OK.
4. You are allowed to have a scientific calculator in the exam. However, graphing calculators are NOT allowed on this exam.
5. No textbook or electronic equipment (other than scientific calculator) allowed.

You can also view the rules that will be printed on the exam cover page.

#### Exam times

You can take the exam up to two times. You can take it once on Thursday, November 15 and once on Thursday, November 29. Each day, the exam is offered at the following times. Plan to take it during the time that you are officially registered. (You can check with a proctor to see if there is a computer available to take the exam at one of the other times, but there may not be extra computers available.)

• 11:15 AM - 12:05 PM
• 12:20 PM - 1:10 PM
• 1:25 PM - 2:15 PM

Exam location: Elliot Hall, room S121

If you take the exam twice, your exam score will be the maximum of your scores from the two attempts.

#### Points and due date summary

Total points: 100
Assigned: Nov. 15, 2018, 11 a.m.
Due: Nov. 29, 2018, 2:30 p.m.
Time limit: 50 minutes