AP Calc AB
AP Calculus AB Name ____________________________________
Basic Integration Test Review
Integrate the following:
1. [pic] 2. [pic]
3. [pic] 4. [pic]
5. [pic] 6. [pic]
7. [pic] 8. [pic]
9. [pic] 10. [pic]
11. [pic] 12. [pic]
13. [pic] 14. [pic]
Approximate the area of the following functions using (a) right endpoints, (b) left endpoints, (c) midpoints and (d) trapezoidal approximation in the given intervals using the given number of sub-intervals. Do not use programs or graphing capabilities on your calculator.
15. [pic]; [2, 4] n = 6 16. [pic], [1, 9] n = 4
Use definite integration to find the exact area bound by[pic], the x-axis and the given interval:
17. [pic]; [0, 3] 18. [pic]; [3, 15]
19. [pic]; [e, e2] 20. [pic]
21. A particle moves along the x-axis such that its velocity at any time (t) is given as [pic]; [0, 4]. Find:
A) Total distance the particle traveled in the first 4 seconds.
B) Displacement in the first 4 seconds.
C) The acceleration of the particle at 3 seconds.
D) Total distance the particle traveled in the first 3 seconds.
E) Displacement in the first 3 seconds.
F) The acceleration of the particle at 1 second.
G) What is the average velocity of the particle over the 4 second interval?
22. A particle moves along the x-axis such that its velocity at any time (t) is given as [pic]; [1, 5]. Find:
A) Total distance the particle traveled in the first 5 seconds.
B) Displacement in the first 5 seconds.
C) The acceleration of the particle at 2 seconds.
D) Total distance the particle traveled in the first 3 seconds.
E) Displacement in the first 3 seconds.
F) The acceleration of the particle at 4 second.
G) It is known that the position of the particle at t = 0 is -17. What is the position of
the particle at t = 5 seconds?
H) What is the average velocity of the particle in the first 4.5 seconds?
23. The rate at which the number of people inside CB South changes between 6:40 am and 7:20 am is given by the function [pic]. At 6:40 am where t is the number of minutes that has elapsed since 6:40 am. It is known that at 6:40, there are 57 people in the building.
A) How many people per minute are entering the building at 7:10 am?
B) How many people are present in the building at 7:20 am?
C) What is the average rate at which people enter the building between 7:05 am and
7:20 am?
24. Consider the differential equation [pic]. Let [pic]be the particular solution to the given differential equation with the initial condition [pic]. Find [pic].
25. Evaluate: [pic] 26. Evaluate: [pic]
27. Evaluate: [pic]
Given: [pic]; [pic]; [pic]
28. Evaluate: [pic] 29. Evaluate: [pic]
30. Evaluate: [pic] 31. Evaluate: [pic]
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.