# 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

When the exam is available, you can take the exam on your computer. Once you begin an attempt, you will have 50 minutes to complete it.

We ask that you take the computer graded exams with no aids other than one (double-sided) sheet of notes and a scientific calculator. (If you don't have a scientific calculator, then we ask that you don't use the graphing or derivative/integral functions of your graphing calculator.)

The exam format will be similar to the Gateway Exam. The exam will not tell you if you got the problems correct or incorrect, but will simply say that the answer was received and show you how it interpreted your response.

When you are finished with an exam attempt, you can go to your gradebook to see your score.

#### Exam times

You can take the exam as many times as you like between 11:00 AM on Thursday, November 19 and 2:30 PM on Thursday, December 3. Click the “Generate new assessment attempt” at the bottom of the exam to get a new exam. If you take the exam more than once, your exam score will be the maximum of your scores from the attempts.

#### Points and due date summary

Total points: 20
Assigned: Nov. 19, 2020, 11 a.m.
Due: Dec. 3, 2020, 11:59 p.m.
Time limit: 50 minutes