True/False Quiz for Chapter 7

Further Integration Techniques and Applications of the Integral

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Chapter 7 Summary

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1. The integral of a product is the product of the integrals. True False

2. When using integration by parts, pick something easy to integrate to go in the I column. True False

3. When using integration by parts, you have to get it right the first time. True False

4. To use a table of integrals, your integral must appear in the table. True False

5. To use a table of integrals, you may have to make a substitution to turn your integral into one that appears in the table. True False

6. To use a table of integrals, you may have to use some algebra to turn your integral into one that appears in the table. True False

7. To find the area between the graphs of f and g, integrate their difference. True False

8. To find the area between the graphs of f and g, integrate the larger minus the smaller where possible. True False

9. To find the area between the graphs of f and g, integrate the absolute value of their difference. True False

10. The consumers' surplus represents the total amount that consumers save by paying a lower price. True False

11. The producers' surplus represents the amount extra that each producer will earn by charging a higher amount. True False

12. The average of f on [a, b] is (f(a)+f(b))/2. True False

13. The moving average of f tends to be more volatile than f itself. True False

14. A moving average of f shows long-term trends in f more clearly. True False

15. _a⁺f(x) dx = F() F(a) if F' = f. True False

16. _a⁺f(x) dx may or may not exist. True False

17. _a^bf(x) dx may or may not exist. True False

18. x f'(x) = x² + 1 is a differential equation. True False

19. x f(x) = x² + 1 is a differential equation. True False

20. x f'(x) = x² + 1 has as a solution f(x) = x + ln x + C. True False