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Definite Integrals Chapter Exam

Exam Instructions:

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

Page 1

Question 1 1. Which of the following represents the area of the FIRST rectangle being used to estimate the area under the curve f(x) between x = 0 and x = 2 when divided into 4 slices?

Question 2 2. How many terms are in the Riemann sum represented below?

Question 3 3. You are going to take a Riemann Sum of the area below. To do this, you divide the region into four slices of equal width. How wide is each slice?

Question 4 4. Using the single term Riemann sum as shown, what is the area beneath the curve f(x) between 0 and two pi?

Question 5 5. Estimate the area beneath the curve f(x) using the two term Riemann sum as shown below.

Page 2

Question 6 6. Express 7 • 6 • 5 • 4 • 3 • 2 • 1 as a factorial.

Question 7 7. Find 11!/8!

Question 8 8. What are the common factors between 7! and 5! ?

Question 9 9. How many ways can you arrange 3 plants on a shelf from a selection of 8 different plant types?

Question 10 10. A club is electing four officers from a group of 20 people. How many different sets of officers can be elected?

Page 3

Question 11 11. Which of the following integrals represents the area under the graph below?

Question 12 12. What's the integral of the function f(x) with respect to x evaluated between the point A and the point B?

Question 13 13. Which of the following graphs shows the correct region of integration for the integral below?

Question 14 14. Given f(x) on the graph, what does z equal?

Question 15 15. Given f(x) on the graph below, which of the following integrals will equal 0?

Page 4

Question 16 16. Given a continuous function f(x) that satisfies the equation below, which of the following is true, according to the average value theorem?

Question 17 17. The average value for this continuous function over the shaded region is 2. According to the average value theorem, how many times does this function pass through the value 2?

Question 18 18. Given that the function f(x) has an average value of 4 over the region x = 5 to x = 10, will there be a value of x over this region where f(x) = 4? Why or why not?

Question 19 19. Use the average value theorem to determine the average value of g(s) between s=0 and s=5.

Question 20 20. Use the average value theorem to determine the average value of f(x) between 0 and 2.

Page 5

Question 21 21. Which of the following answers is the solution for the gamma function of 1/2.

Question 22 22. Using the factorial representation of the gamma function, which of the following answers is the solution for the gamma function Γ(n) when n = 8?

Question 23 23. Which property of the gamma function is known as the duplication formula?

Question 24 24. Which of the following is an integral representation of the gamma function?

Question 25 25. What is another name for the gamma function?

Definite Integrals Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

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