Definite Integrals Practice Problems for AP Calculus

Review the following concepts if needed:

• Riemann Sums and Definite Integrals for AP Calculus
• Fundamental Theorem of Calculus for AP Calculus
• Evaluating Definite Integrals for AP Calculus
• Improper Intervals: Infinite Intervals of Integration and Infinite Discontinuities for AP Calculus

Part A The use of a calculator is not allowed.

Evaluate the following definite integrals.

1. 
2. 
3. 
4. 
5. 
6. 
7. If f' (x )=g (x ) and g is a continuous function for all real values of x , express
8. 
9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. Use a midpoint Riemann sum with four subdivisions of equal length to find the approximate value of
17. Given
    1. 
    2. 
    3. 
    4. 
18. 
19. 
20. Let f be a continuous function defined on [0, 30] with selected values as shown below:



Use a midpoint Riem ann sum with three subdivisions of equal length to find the approximate value of

21. 
22. 
23. 
24. 
25. 

(Calculator) indicates that calculators are permitted.

31. 
32. 
33. The graph of f' , the derivative of f' , 6 ≤ x ≤ 8 is shown in Figure 11.7-1.



1. Find all values of x such that f attains a relative maximum or a relative minimum.
2. Find all values of x such that f is concave upward.
3. Find all values of x such that f has a change of concavity.
34. (Calculator) Given the equation 9x² +4y² – 18x +16y =11, find the points on the graph where the equation has a vertical or horizontal tangent.
35. (Calculator) Two corridors, one 6 feet wide and another 10 feet wide meet at a corner. See Figure 11.7-2. What is the maximum length of a pipe of negligible thickness that can be carried horizontally around the corner?



36. Evaluate
37. Determine the speed of an object moving along the path described by x =3 – 2t²,



38. 

Solutions for these practice problems can be found at: Definite Integrals Solutions to Practice Problems for AP Calculus