▪ Further Integration Techniques and Applications of the Integral

 Ερωτήσεις Σωστό - Λάθος

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  

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